Step 1: Preheat your oven to 375°F (190°C). Lightly butter a 9x13-inch baking dish.
Step 2: Peel and thinly slice the potatoes. Rinse them under cold water to remove excess starch, then pat thoroughly dry with paper towels.
Step 3: In a large saucepan or Dutch oven, melt 4 tablespoons of unsalted butter over medium heat. Add the minced garlic and cook for about 1 minute until fragrant, being careful not to brown it.
Step 4: Whisk in the all-purpose flour and cook for 1-2 minutes, stirring constantly, to create a roux.
Step 5: Gradually whisk in the whole milk and heavy cream, a little at a time, ensuring no lumps form. Bring the mixture to a gentle simmer, whisking frequently, until the sauce begins to thicken and coats the back of a spoon (about 5-7 minutes).
Step 6: Remove the saucepan from the heat. Stir in 1.5 cups of the shredded sharp cheddar cheese and 1 cup of the shredded Gruyère cheese until completely melted and smooth. Season generously with salt, black pepper, and a pinch of nutmeg. Taste and adjust seasoning as needed.
Step 7: Arrange a single layer of sliced potatoes in the prepared baking dish, slightly overlapping them. Pour about one-quarter of the cheese sauce evenly over the potatoes. Sprinkle with a portion of the remaining cheddar and Gruyère cheese. Repeat this process, creating 3-4 layers, ending with a final layer of potatoes topped with the remaining sauce and a generous sprinkle of both cheeses.
Step 8: Cover the baking dish tightly with aluminum foil. Bake for 45-60 minutes, or until the potatoes are mostly tender when pierced with a knife.
Step 9: Remove the foil. Increase the oven temperature to 400°F (200°C) or switch to broiler mode (watching carefully!). Continue baking uncovered for another 15-20 minutes, or until the top is bubbly, golden brown, and slightly crispy.
Step 10: Let the scalloped potatoes rest for 10-15 minutes before serving. This allows the sauce to set and prevents it from being too runny.