Begin by washing and peeling the Yukon Gold potatoes, then slice them into uniform 1/8-inch rounds using a mandoline for even cooking. Arrange the slices in a bowl of cold water to prevent browning.

While you prepare the potatoes, preheat your oven to 350°F (175°C).

In a large saucepan, melt 4 tablespoons of unsalted butter over medium heat. Add the minced garlic and diced onion, sautéing for 1-2 minutes until fragrant. Stir in 1/4 cup of flour to create a roux, and cook for another minute. Gradually whisk in 2 cups of whole milk and 1 cup of chicken broth, bringing the mixture to a boil until it thickens.

In a greased 9x13 inch baking dish, layer the sliced potatoes, covering the bottom with a layer. Spoon a generous amount of the cheese sauce over the potatoes and repeat until you have three layers.

Cover the baking dish tightly with aluminum foil and bake in the preheated oven for 30 minutes.

After 30 minutes, carefully remove the foil and bake for an additional 35-45 minutes until the top is golden brown and edges bubble.

Let the dish cool for 10 minutes before serving, allowing the sauce to set.