usage - How do you say "You have gotten better at X"?

I was just reminded on another site that "being good at something" is expressed as [上手]{じょうず}/[上手]{うま}い, not いい. How do you tell someone they "have gotten better at something"? Xさん, 料理することがもっと上手いですね。 would be my thought. Is that right? Would that be the way a native would say it? Is that even how a textbook would word it?

Answer

You can use なる (to become) to indicate change, as follows:

うまくなる (い-adjective, い->く)
上手になる (な-adjective + に)

These both mean "to become good/skilled".

Then for "to become more skilled" you can use もっと, さらに or 前より:

もっと上手になる to become better
さらに上手になる to become even better

前より上手になる to become better than before