This excerpt is taken from Sheikh Muhammad Farooq's book Issues of the Two Eids.
It is preferable to eat the meat of the sacrifice after the Eid prayer on the day of Eid al-Adha.
Eating the meat of the sacrifice after finishing the Eid prayer on the day of Eid al-Adha is a Sunnah and recommended practice.
Buraidah bin Hushaib (may Allah be pleased with him) narrates:
كان النبى صلى الله عليه وسلم لا يخرج يوم الفطر حتى يطعم، ولا يطعم يوم الأضحى حتى يصلي
“The Prophet (peace be upon him) would not go out for the Eid al-Fitr prayer until he had eaten something, and on the day of Eid al-Adha, he would not eat anything until he had performed the prayer.”
Reference: Musnad Ahmad: 360/5 - Jami` at-Tirmidhi, Chapters of the Two Eids, Chapter on Eating on the Day of Fitr before Going Out: 542 - Ibn Majah, Book of Fasting, Chapter on Eating on the Day of Fitr before Going Out: 1756 - Mustadrak Hakim: 295/1 - Its chain is Hasan, Thawab bin Utbah Mahri, a truthful and good narrator.
It is narrated from Buraidah bin Hushaib (may Allah be pleased with him), who said:
أن النبى صلى الله عليه وسلم لا يخرج يوم الفطر حتى يطعم، وكان لا يأكل يوم النحر شيئا حتى يرجع فيأكل من أضحيته
“Indeed, the Prophet (peace be upon him) would not go out for the Eid al-Fitr prayer without eating something, and on the day of Eid al-Adha, he would not eat anything until after finishing the prayer, returning home, and then eating from his sacrificial meat.”
Reference: Dar Qutni: 1697 - Its chain is Hasan
Nafi’ (may Allah have mercy on him) narrates:
أن ابن عمر كان يوم الأضحى يخرج إلى المصلى، ولا يطعم شيئا
“Ibn Umar (may Allah be pleased with both of them) would head to the Eid prayer ground on the day of Eid al-Adha without eating anything.”
Reference: Bayhaqi: 283/3 - Its chain is Sahih
Benefits:
Imam Tirmidhi, may Allah have mercy on him, states that the scholars have deemed it recommended to eat after returning from the Eid prayer on the day of Eid al-Adha.
Reference: Tirmidhi under Hadith: 542
Ibn Qudamah, may Allah have mercy on him, says: The wisdom behind delaying eating on the day of Eid al-Adha is that on this day, performing the sacrifice and eating from the meat of the sacrifice is a prescribed act. Therefore, breaking the fast (having breakfast) with the meat of the sacrifice on this day has been made permissible.
Reference: Al-Mughni by Ibn Qudamah with Al-Sharh Al-Kabeer: 229/2 - Nayl Al-Awtar: 307/3 - Tuhfat Al-Ahwazi: 3/68
Explanation of a Weak Hadith:
It is narrated from Buraidah رضي الله عنه that he said:
كان رسول الله صلى الله عليه وسلم إذا كان يوم الفطر يخرج حتى يأكل شيئا، و إذا كان الأضحى لم يأكل شيئا حتى يرجع، وكان إذا رجع أكل من كبد أضحيته
“When it was the day of Eid al-Fitr, the Messenger of Allah صلى الله عليه وسلم would not leave the house until he had eaten something, and on the day of Eid al-Adha, he would not eat until he had performed the prayer and returned home. When he returned home, the Prophet صلى الله عليه وسلم would eat the liver of his sacrifice (i.e., kebab).”
Reference: Bayhaqi: 283/3 – Its chain is weak; Aqbah bin Abdullah Asamm is weak and a narrator who conceals defects, and in this narration, there is also concealment by him.
Since this narration is weak, it is not correct to deduce from it that eating the liver of the sacrifice specifically after finishing the Eid prayer is prescribed. Rather, choosing any part of the sacrificial meat is Sunnah.
