I think one of the first questions we should be asking ourselves after the flop min raise is whether or not we want to get it all in with TPTK? If the money does end up going in then I'm not sure we want to be the one making the raises.

If you think there is a good chance he is bluffing and also considering our our table image (he may think we're just trying to pick up another pot on an ace high board and thus decide to play back) I would lean towards calling the bet and letting him make a double barrel bluff on the turn. If he does this and makes another big bet on the river that would be a tough spot.

If we raise the flop then his range for continuing becomes narrower and stronger, we're stopping him from bluffing again most of the time, and we're getting called by better hands a lot more often than worse hands.

Not sure if any of this is correct but these were my first thoughts when I saw the hand.