A comma isn't necessary there.

"What's funny" is a noun phrase. It's similar to, for instance, "what you need" (which is a noun clause btw).

A loan is what you need.

So:

Cat's dry humor is what's funny.

It's the same thing inverted:

What's funny is Cat's dry humor.

A comma isn't necessary there.

"What's funny" is a noun clause. It's similar to, for instance, "what you need."

A loan is what you need.

So:

Cat's dry humor is what's funny.

It's the same thing inverted:

What's funny is Cat's dry humor.