I cook hard boiled eggs with shells in meat cholent and was wondering if I could eat them during the nine days. If cooked before Rosh Chodesh Av or after - would that make a difference?
וכבר נתפשט המגהג שלא לאכול אפילו תבשיל שנתבשל בו בשר. אבל מותר לאכול תבשיל שיתבשל בקדרה של בשר.
The custom to not eat even a cooked item that has been cooked with meat has already become popular. But it is permissible to eat a cooked item that was cooked in a meat pot.
Since the issue is eating meat during the nine days, I don't think it makes a difference when the meat was prepared.
this egg - a tavshil shel bassar (although excluded by the Shulchan aruch) is included in the 9 days prohibition by the vast majority of Ashkenazic poskim as well as several contemporary sefardic ones as well - similar to laws of meat and milk.
see this excellent comprehensive article by rabbi Y. spitz addressing this exact issue (in the postscript):
Even according to those who have the custom to refrain from consuming meat during these days, this is permitted according to many authorities.
The Orehot Hayyim (Vol. 1: Hilkhot Tishah B'av: 4) writes:
ויש נמנעין מאכילת בשר משנכנס אב לפי שאין שמחה אלא בבשר ואע"פי כן אין צריך להמנע מתבשיל שנתבשל בו בשר
There are those who refrain from the consumption of meat from the beginning of Av, for joy is only experienced through the consumption of meat. But nevertheless, one need not refrain from a food which was cooked with meat.
This is cited by the Beit Yosef (OH 551:10) as well, who presents no dissenting view, and he cites this opinion in the Shulhan Arukh (there) as well.
The Taz (551:11) clarifies that this includes not just foods cooked with meat, but even the meat's gravy.