I think this is correct. You want to be fattening the pot while you are ahead.
I scrolled down your post and was surprised you didnt check raise.
IMO checking here and flatting the Cbet is advanced post-flop play that gets into trouble spots.
So , im interested in why you chose this line.
Did you not raise the flop bet because it exposes your Set ?
Do you think this line is the way to go versus this 10/10 villian ?