Hey, I just want to point out, this is a classic example of mekalkel(the shells get tossed after and can't be used for anything). It is permitted(since it is also davar sh'eino mitkaven). Sephardim are lenient. To prove it's mekalkel, the shells get thrown away! See Yalkut Yosef Shabbat 340:9. I'm only making this point because it's very inconvenient and may be unnecessary to worry about as a stringency. The source mentioned isn't explicit about eggs, but I'm sure the din is the same. A better source would be the psak about letters on cakes & shabbat; permitted there, too. —
chacham Nisan 40 mins ago