I like to shove in this sort of spot. It's definitely +ev.

If you check, which is fine if he doesn't limp in this spot much, then I would bet almost any flop he checks to me on 1/2pot.

I might not bet A x x cause he should know I'm shoving ax preflop.

Flops like Q x x and K x x I'm betting.

Junk flops where a random hand in bb is likely to hit are fine to bet to.

Start betting here with atc and you will be surprised on how often you take it down.

If you shove and he calls, oh well, win the 60/40 or fire up another mtt.