Tough spot for sure. Defending oop on this board seems very difficult because of how hard our UTG open/call-range misses it. I don't think we can have a flop raising range unless it's an exploit, since it's so hard for us to have something worth value raising. Not like villain nails this flop either obviously, but a sizable part of his range is AAxx which is quite a monster here (if our range is say $fi15!$4b4, pocket AAAA has 64% equity vs our range otf!).

Leading doesn't make much sense either, so I think we defend the board by check/calling and going from there. This hand def seems worth continuing. We have 46% against a range of $3b6i (and a lot of people prob cbet all of their air here, which might even be fine given how hard we miss?), and having the gs + good backdoor draws is important since we ofc want to be able to hit those draws as well to be less capped on later streets.

Turn/river play is obv gonna be shitty with our range kind of face up as mostly overpairs with some low card stuff in the mix. It's kinda close to polarized ranges in NL I think, though the equities shift more based on turn cards. Intuitively with this hand I think we want to continue mainly when we turn a decent draw and usually give up on blank turns. Would guess we want to start with a check on turn as well since I don't see many cards improving our range hard enough to warrant a lead (though a small HSNL type protection/"f your air hands"-lead could make sense on some cards maybe? this hand might fit well into such a range to realize the gs + set outs + w/e cheaply?).

FWIW I'm really not sure at all about most of the above. Just my initial thoughts, and I could easily have gotten something wrong. Very interested in hearing some other perspectives as well.

just call the flop and put in some aggression on turn cards that improve your hand or range. I don't see a ton of value to x/ring the flop because villain's continuing range is typically well ahead and we're in a bad spot on turn blanks as our equity will drop significantly against villains stacking range.

I guess the best way to balance a flop call with some stronger hands would be to include a few sets. I worry about creating a weak range on flops OOP in 3bet pots, but I'm not sure that there is a better option than calling on the flop.