Preheat the oven to 425 degrees F (220 degrees C). Line a baking sheet with parchment.
Place salmon on the prepared baking sheet; drizzle with olive oil and season with salt and pepper.
Bake in the preheated oven until salmon flakes easily with a fork, about 15 minutes. Cooking time will vary based on thickness of filets.
Meanwhile, for sauce, melt butter in a saucepan over medium-low heat. Add garlic and cook just until fragrant, about 30 seconds.
Stir in milk and cream; simmer for 2 to 3 minutes.
Lower heat to very low. Add Swiss cheese and Parmesan cheese in small handfuls, whisking constantly until melted; remove from heat.
Stir in lemon zest. Add lemon juice slowly to taste; season with salt and white pepper. Garnish with parsley.
