**Preheat the Oven:**
- Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish and set aside.
**Prepare the Sauce:**
- In a medium saucepan over medium heat, melt the butter. Stir in the flour and cook for 1 minute, whisking continuously, to form a roux.
- Gradually whisk in the heavy cream and milk until smooth. Cook for 3–4 minutes, or until the mixture begins to thicken.
- Add garlic powder, onion powder, nutmeg, salt, and pepper. Stir well.
**Add the Cheeses:**
- Remove the saucepan from heat and stir in the cheddar, Gruyère, and Parmesan cheeses. Whisk until smooth and fully melted.
**Assemble the Dish:**
- Arrange half of the sliced potatoes in the prepared baking dish, slightly overlapping them. Pour half of the cheese sauce over the potatoes.
- Repeat with the remaining potatoes and sauce, ensuring all slices are covered.
**Bake:**
- Cover the dish with aluminum foil and bake for 45 minutes. Remove the foil and bake uncovered for an additional 15–20 minutes, or until the potatoes are tender and the top is golden and bubbly.
**Serve:**
- Allow the dish to cool for 5 minutes before garnishing with chopped parsley, if desired. Serve warm.