Step 1: Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish.
Step 2: In a large saucepan or Dutch oven, melt the butter over medium heat. If using, add minced garlic and cook for 1 minute until fragrant. Whisk in the flour and cook for 1-2 minutes, stirring constantly, to create a roux.
Step 3: Gradually whisk in the warmed milk, a little at a time, ensuring no lumps form. Continue whisking until the sauce begins to thicken, about 5-7 minutes.
Step 4: Remove the saucepan from the heat. Stir in the salt, black pepper, and nutmeg. Add 1.5 cups of the shredded sharp cheddar cheese and all of the Gruyere cheese, stirring until melted and smooth. Reserve the remaining 1/2 cup sharp cheddar and Parmesan for later.
Step 5: Arrange a layer of potato slices evenly in the bottom of the prepared baking dish. Pour about a third of the cheese sauce over the potatoes. Repeat layering with potatoes and sauce two more times, ending with a layer of sauce.
Step 6: Cover the baking dish tightly with aluminum foil. Bake for 45 minutes. Remove the foil, then sprinkle the remaining 1/2 cup sharp cheddar and the 1/2 cup Parmesan cheese evenly over the top.
Step 7: Return to the oven, uncovered, and bake for another 15-30 minutes, or until the potatoes are tender (a knife should easily slide through them) and the cheese topping is bubbly and golden brown.
Step 8: Remove from the oven and let the cheesy scalloped potatoes rest for 10-15 minutes before serving. This allows the sauce to set and makes for easier serving.