Good guy UTG (22/11 with a 725 stack) opens to 15.
I call with OTB with a 965 stack
BB comes along. He is 27/14 and has a 550 stack - he seems good.

Flop (45)
BB checks, UTG bets 40, I call, BB CR to 105, UTG fold, I raise to 225, he shoves making it 535 total.
I have not seen him do that before.

What to do?

Edited: I got the action mixed up.....

So you called, then raised BB's CR from 105 to 330?

If so...what did villain do after that?

what hand does that BB have that we beat there? T9? T6 96 is unlikely, he wouldn't slow play/felt JJ+ preflop if he is good with 3 players to the flop. JQ and pair+draw hands are possible but we eliminate that with just a call on flop. I'm not sure what hand he felts here into field of 2 players that we beat
If he has str8, we draw to FH with decent implied odds. If a 8 or J falls on turn, he might slowdown even with str8 sometimes(78x hands) so we can boat up cheaper. honestly, we beat here only pure bluffs, T9 type hands and occasional draws if he is any good.
EDIT:
However, we need to play for stacks if he is willing to play for stack T9o, T9s or JTs here..
Its kinda close. If we eliminate draws, which are for most part unlikely due to fishy re raise on flop, we still need to go broke if he is gonna felt just top two every time. I'm not sure if he calls T9o into a raise . If he doesn't then we are quite behind here.

He felts T9 almost certainly.

I was actually BB in this hand.
I had top set with TT. He called, and I won one of the largest pot I ever won.
The turn came , and the river so not getting it all in on the flop would likely have resulted in less action.

I actually thought I played it pretty bad - at first.
I was rather certain that button (hero as described) didn't have the flopped straight, since I hadn't seen him play any SC to a raise before. I had him on an overpair, lower set, or as a remote possibility AJ.

But I though the fishy re-raise to 105 would give away my hand and make him realise he was beat.

From your comments it doesnt seem as clear.

I know a lot of you would recommend leading out with a set. I have done that a lot and people have a tendency to fold pretty often. (I need to do that as a bluff more often to get called)