(some explainations from "Peshawar Nights" book)
Source
... Another proof of the Prophet's preferring Ali to other men is the "Hadith of the Bird" (Hadith-e-Ta'ir). This hadith is so well known and so commonly accepted that we need not mention all its sources. I will mention only some of them.
HADITH OF THE ROASTED BIRD
Most of your prominent ulema, like Bukhari, Muslim, Tirmidhi, Nisa'i, and Sijistani in their Siha, Imam Ahmad Bin Hanbal in his Musnad, Ibn Abi'l-Hadid in his commentary on Nahju'l-Balagha, Ibn Sabbagh Maliki in Fusulu'l-Muhimma, and Sulayman Balkhi Hanafi in Yanabiu'l-Mawadda, Chapter 8, and a host of other reliable authors have recorded the hadith-e-Ta'ir in their works. They verify that this hadith was reported by 24 narrators of hadith from Anas Bin Malik. Ibn Sabbagh Maliki in his Fusulu'l-Muhimma writes about it in these words: "In the books of authentic hadith and reliable narrations, the hadith-e-Ta'ir from Anas Bin Malik is indisputably correct." Sibt Ibn Jauzi, on page 23 of his Tadhkira, and Sunan of Tirmidhi and Mas'udi on page 49 of Volume II of Muruju'dh-Dhahab, have focussed especially on the last part of this hadith which contains the Prophet's prayer and its acceptance by Allah. Imam Abu Abdu'r-Rahman Nisa'i in the 9th hadith of his Khasa'isu'l-Alawi, and Hafiz Bin Iqda and Muhammad Bin Jarir Tabari have all referred to the unbroken chain of narrators and to the authentic sources of this hadith, saying that it was narrated by 35 companions of the holy Prophet from Anas Bin Malik. In short, all your distinguished ulema have verified the authenticity of this hadith and have included it in their books. Allama Seyyed Hamid Husain has dedicated an entire volume of his Abaqatu'l-Anwar to this hadith. He collected all reliable sources from your distinguished ulema and clearly proved the authenticity of this hadith.
According to this hadith, one day a woman brought a gift of a roasted bird to the Prophet. Before eating it, the Prophet, raising his hands, invoked Allah thus: "O Allah! Of your whole creation, send the person who is the dearest to you and to me, so that he may partake of this roasted bird with me."
Ali then came in and ate the roasted bird with the Holy Prophet.
Some of your books, such as Fusulu'l-Muhimma of Maliki, Ta'rikh of Hafiz Nishapuri, Kifayatu't-Talib of Ganji Shafi'i, and Musnad of Ahmad bin Hanbal, etc., in which the hadith has been reported from Anas bin Malik, have recorded that Anas said: "The Prophet had not finished his invocation when Ali came into the house, but I kept the matter secret. When Ali stamped his foot the third time, the Prophet ordered me to let him in. When Ali entered, the Prophet said: 'Allah's Mercy be upon you; what brings you to me?' Ali then told him that he came to him three times but was allowed entrance only this time. The Prophet asked what made me behave like that, and I replied: "The truth is that, on hearing your invocation, I wished that such an honor might fall to the lot of someone of my tribe." Now I ask you respected people whether the invocation of the Holy Prophet was accepted or rejected by Allah.
Sheikh: Obviously Allah accepted it since He has promised in the Holy Qur'an that He would accept the Prophet's invocation. Moreover, Allah knew that the Prophet would not make an inappropriate request. So Allah always accepted his invocation.
Well-Wisher: Allah sent Ali, the most deserving person in His creation, to the Prophet. Your own scholars have confirmed this event. Muhammad bin Talha Shafi'i has in his Matalib-us Su'ul, Chapter 1, Part 5, page 15, established the high position of Ali as the beloved of Allah and of the Prophet on the basis of the hadith of Ensign (Rayat) and the hadith of the Bird (Ta'ir). In that connection he says: "The intention of the Prophet was that the people should understand the unique and high distinction of Ali, who attained the highest pinnacle to be reached by the pious." Also Hafiz and Muhammad Bin Yusuf Ganji Shafi'i (died 658 A.H.) writes in his Kifayatu't-talib, Chapter 33, referring to the virtues of Ali Bin Abi Talib, that this hadith clearly proves that Ali was the dearest person in creation to Allah. Later he says that Hakim Abu Abdullah Hafiz Nishapuri related this hadith-e-Ta'ir of Anas from 86 narrators and also recorded the names of all 86 narrators. (See Kifayatu't-Talib, Chapter 32). That "hadith" quoted by you, in comparison with the hadith narrated by your own high-ranking ulema (excepting a few stubborn fanatics), cannot be relied upon and would be rejected by learned men.
Sheikh: I'm afraid that you have made up your mind not to accept what we say.
Well-Wisher: How can you attribute such bias to me? Can you cite a single instance in which you have put forward a cogent argument and I have unreasonably rejected it? I swear that in religious debates with the Jews, the Christians, the Hindus, and the Brahmins, the ignorant Baha'is in Iran, the Qadanis in India, and the materialists - in all of these circumstances, I never acted obstinately in my argument. I never adopted a refractory attitude towards these unbelievers - how could I do so with you, my brothers in Islam?
Sheikh: We read the account of your debate with the Hindus and Brahmins of Lahore in the newspapers. We were greatly impressed by it. Although we had not met you, we felt we were morally affiliated with you. I hope that Allah will lead you and us to the right path. We believe that if there is any doubt about a certain hadith, we should, according to your proposal, refer it to the Holy Qur'an. However, if you question the excellence of Caliph Abu Bakr and the mode of caliphate of the major caliphs, and if you consider the hadith dubious, will you also hesitate to believe an argument based on the verses of the Holy Qur'an?
Well-Wisher: May Allah not grant us the day when we doubt facts based on the Holy Qur'an or authentic hadith. However, when we have entered into a religious debate with any nation or community, they also argued from the verses of the Holy Qur'an to establish their point of view. Since the verses of the Holy Qur'an have various levels of meaning, the last Prophet, in order to guard the people against misunderstanding, did not leave the Holy Qur'an as the sole source of guidance. As has been acknowledged by both sects (Shias and Sunnis), he himself said: "I leave with you two great things: the Book of Allah (Qur'an) and my descendants. If you are attached to these two, never, never shall you go astray after me. Verily, these two shall never be separated from one another until they meet me at the Fountain of Kauthar." For this reason, the meaning of the revelation of the Holy Qur'an should be sought either from the Prophet, the primary interpreter of the Holy Qur'an, or after him, from the equals of the Holy Qur'an, the holy descendants of the Prophet. The Holy Qur'an says: "So ask you the people of the Remembrance if ye know not." (21:7)