Preheat your oven to 375°F (190°C) and lightly grease a 9x13 inch baking dish.

Arrange half of the sliced potatoes in a single layer at the bottom of the prepared baking dish.

In a medium saucepan, melt the butter over medium heat. Stir in the flour and cook for 1 minute, whisking constantly, until a smooth paste forms.

Gradually whisk in the warm milk until the mixture is smooth and thickened. Stir in salt and pepper, then bring the sauce to a gentle simmer, stirring occasionally, and remove from heat.

Pour half of the prepared sauce evenly over the potatoes in the baking dish. If using, sprinkle half of the shredded cheese over the sauce.

Layer the remaining sliced potatoes over the sauce and cheese, then pour the remaining sauce over the second layer of potatoes.

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

Remove the foil, and if desired, sprinkle with the remaining cheese. Continue baking for another 30-40 minutes, or until the potatoes are tender and the top is golden brown and bubbly.

Remove from oven and let stand for 10 minutes before serving.