imo there are really only two ways of playing this, and both depend on villain.
Exploitative: get to showdown vs passive/loose players with what is likely the best hand but too thin to get any value. No need to worry about balance because villain is retarded.
GTO: cbet flop and appropriate turn/rivers given reads on villain vs more thinking players because TT-/Jx are the only
hands we ever check back flop with, and villain can play perfectly/really well against us when we define our range as such by checking back.