Is it authentically established that the Prophet (peace be upon him) ate cooked onions or garlic, based on the hadith: "If you must eat them, then render them dead by cooking"?

The aforementioned Hadith (definition) is authentic, narrated by Muslim, and indicates that the Prophet, peace be upon him, did not eat garlic raw because he converses with one whom no one else converses with. However, it is not forbidden. The Malikis and Shafi'is have explicitly stated the prohibition of eating raw garlic and onions for the Prophet, peace be upon him, due to their strong odor. If cooked, it is permissible to eat them, as it has been reported that he, peace be upon him, ate food containing cooked onions. It was also narrated that he, peace be upon him, said: "Whoever eats them, let him cook them thoroughly." Cooking removes the unpleasant odor.