Preheat the oven to 400ºF (200°C). Line a baking sheet with parchment paper or foil. In a shallow plate, mix together the Parmesan, garlic, paprika, parsley, salt, and pepper.
Arrange the halibut fillets on the center of the baking sheet and place trimmed asparagus around the fish. Drizzle the halibut fillets with olive oil, then sprinkle the cheese mixture over the halibut, pressing it in lightly with your fingers. Season asparagus with salt, pepper, any leftover cheese mixture.
Bake until the fish is opaque in the thickest part, about 15 minutes. You can crisp up the parmesan crust for 1 minute under the broiler if you like. Serve the baked halibut with lemon slices.