expression, ichidan verb
have a refined palate; be used to eating the best
Describes someone whose taste in food has become discerning through experience with high-quality cuisine; often implies being hard to please with ordinary fare.
彼は世界中の高級料理を食べてきたので、口が肥えている。
He has eaten fine cuisine from around the world, so he has a refined palate.
口が肥えた人でも満足できる味だ。
It's a flavor that can satisfy even someone with a discerning palate.