In a large skillet over medium heat, melt 1 tablespoon each of butter and olive oil. Add mahi-mahi and season with salt and pepper. Cook until golden, 4 to 5 minutes per side. Transfer to a plate.
To skillet, add remaining 1 tablespoon oil. Add asparagus and cook until tender, 2 to 4 minutes. Season with salt and pepper and transfer to a plate.
To skillet, add remaining 2 tablespoons butter. Once melted, add garlic and red pepper flakes and cook until fragrant, 1 minute, then stir in lemon, zest, juice, and parsley. Remove from heat, then return mahi-mahi and asparagus to skillet and spoon over sauce.
Garnish with more parsley before serving.