Signing (or refusing to sign) legislation is a good example of the President exercising executive power. I'm not aware of any occasion when the President delegated that power to Congress (or to the Supreme Court). Can you cite something?

Maybe we have a misunderstanding. I'm not asking a kind of broad speculative question like "hypothetically, what could a hardcore monarchist say to critique our constitutional system?"

I was asking for a plain old real-world example of delegation of power from the executive branch to another branch. In the real history of the USA. Agreed on one point, though: I can't think of one either.