[well named]

You don't have any read on UTG, but with BB's stats I don't think he's min-raising that flop with someone to act behind except with a hand he wants to build a big pot with, so having the nuts I'd go ahead and accomodate him. I doubt he's folding as much as you think he is. UTG's range is similarly draws or 2 pair+ hands but it's unlikely a larger raise folds them both out, and it's also quite possible that if UTG does have a draw that he'll feel he has too good of odds to fold after BB calls.