Preheat the oven to 425°F. Peel the potatoes and cut them into 1/4-inch thick slices.
Melt 1 tablespoon of the butter over low heat in a large oven-proof skillet. Add the garlic and distribute evenly over the bottom pan. Place a single layer of potato slices in the pan, season with salt and pepper, and repeat with remaining potatoes, making sure to season between the layers.
Separately heat 1 cup of milk and pour it over the potatoes. Add more milk as needed, to come 3/4 of the way up the layers of potatoes. Bring the mixture to a simmer on top of the stove.
Cut the remaining 2 tablespoons of butter into 1/4-inch pieces and distribute evenly over the top. As soon as the top layer of butter has melted, place the pan in the oven and bake for 20 to 30 minutes, or until the potatoes are tender when pierced with a knife and the top is bubbly and brown.
Notes
Quick Recipe Variations:
Sprinkle fresh thyme leaves between the potato layers for extra flavor.
Grate some parmesan cheese between the potato layers and on top.
Top with crumbled bacon and grated cheddar cheese.