Combine butter and olive oil in a large saucepan and cook over medium heat, swirling the pan occasionally, until butter is melted.

Add shallot and cook, stirring frequently, until softened.

Reduce heat to low and gradually whisk in heavy cream until combined. Stir frequently until thickened (mixture will coat the back of a spoon.

Add parmesan, salt, pepper, and nutmeg and stir well until cheese is melted.

Taste-test and add additional spices if needed. Serve over pasta or as desired, or allow to cool and store for later use.