In a small saucepan over medium heat, combine the heavy cream, garlic, and nutmeg and warm for 2 minutes, stirring occasionally, until fragrant and just beginning to steam.
Arrange the asparagus in a single layer in the prepared baking dish.
Sprinkle the salt, pepper, and red pepper flakes onto the asparagus.
Pour the warm cream mixture over the asparagus.
Sprinkle the parmesan, Gruyere, and mozzarella cheeses on top.
Bake for 20 minutes, until the cheese is golden and bubbling and the asparagus is tender.
Garnish the asparagus with chopped parsley before serving.