Preheat the Oven: Set your oven to 375 degrees F (190 degrees C).
Prepare Potatoes: Arrange the sliced potatoes in a buttered 5-inch baking dish, or another dish of a similar size. Set it aside.
Make the Roux: In a 1-quart saucepan, melt butter over medium heat. Add flour and stir continuously for 2 minutes.
Create the Sauce: Gradually stir in milk, continuing to stir frequently. Cook until the mixture becomes smooth and thickens, about 2 minutes.
Add Cheese and Seasonings: Mix in ½ cup of cheese, along with salt and pepper, stirring until the cheese is completely melted.
Assemble for Baking: Pour the cheese sauce over the arranged potatoes. Place the dish on a baking sheet and bake for 25 minutes.
Final Cheese Layer and Bake: After baking, remove the dish from the oven. Top it with 2 tablespoons of shredded Cheddar cheese. Return to the oven and continue baking for another 20 minutes, until the cheese is melted and bubbly.
Notes
Even Slices: Ensure your potato is sliced into even 1/4-inch thick slices, using either a mandoline for precision or a sharp knife. Ensuring the slices are of similar thickness will help them cook uniformly.
Layering: Layer the potatoes and cheese evenly for consistent flavor throughout.