Preheat your oven to 350°F (175°C).

Grate both the cheddar and parmesan cheeses, setting them aside in separate bowls.

Peel and thinly slice the Yukon Gold potatoes into ⅛-inch thick rounds.

In a saucepan over medium heat, melt the butter until bubbling, then add the minced garlic. Cook for 30 seconds until fragrant. Pour in the heavy cream, seasoning with salt and pepper to taste, and bring just to a boil before removing from heat.

Grease your baking dish and begin layering half of the sliced potatoes. Pour half of the creamy garlic sauce over the potatoes, followed by half of the grated cheddar and parmesan cheeses.

Repeat by adding the remaining potato slices, pouring the rest of the cream sauce, and topping with the remaining cheese.

Cover the dish tightly with aluminum foil and bake for 40 minutes.

Remove the foil and continue to bake for an additional 25-35 minutes until the top is golden brown.

Let the dish rest for 5-10 minutes before serving.