1-Preheat the oven to 400°F and grease a 9×13-inch baking dish to prevent sticking.

2-Melt 3 tablespoons of butter in a medium skillet over medium heat. Whisk in 1/4 cup of all-purpose flour and cook for 1 minute to form a roux. Gradually whisk in 1 cup of whole milk followed by 2 cups of vegetable broth, then add 4 grated garlic cloves, 1 tablespoon of chopped fresh thyme, 2 teaspoons of salt, and 1/2 teaspoon of black pepper. Cook while whisking for 2 to 3 minutes until the sauce lightly coats the back of a spoon, and remove from heat to avoid splitting.

3-Layer half of the 3 pounds of sliced potatoes and 1/2 medium thinly sliced onion in the baking dish. Pour half of the sauce on top and sprinkle with 1 cup of shredded sharp cheddar cheese. Repeat the layers with the remaining potatoes, onion, sauce, and 1/2 cup of shredded sharp cheddar cheese for even flavor distribution.

4-Cover the dish with foil and bake for 30 minutes. Remove the foil and bake for another 35 to 40 minutes, until the potatoes are tender and the cheese is browned on top.

5-Allow the dish to stand at room temperature for 20 minutes before serving to let the flavors settle and make it easier to slice.