http://revach.net/article.php?id=3806

Section: Hanhagos   Category: Minhagim
When Should We Eat The Challah From The Eiruv Tavshilin?
The Gemara in Shabbos (117b) says that Rebbi Ami and Rebbi Asi would eat the Challah from Eiruv Tavshilin for Lechem Mishna.  Since they already did one mitzva with it, they wanted to do another.

The Minhag Yisroel Torah brings from the Maharil that he would use the challah from Eiruv Tavshilin for the second uneaten challah of lechem mishna on Friday night and on Shabbos day, and then finally eat it by Seudah Shlishis.  However another minhag is to eat it by the Shabbos day seudah.

The Minhag Yisroel Torah asks what would be the logic in eating it in the morning.  if we want to do as many mitzvos as possible with it then we should have it present at all three meals like the opinion of the Maharil.  The other logical alternative is to eat it right away at the first seudah on Friday night so as to show our love for the mitzva by not delaying.  He offers that the rationale for this minhag is that since Kavod HaYom Adif, the Shabbos day seudah is the most special and honored, therefore we wait for this seudah to honor the Eiruv Tavshilin.