Preheat oven to 375°F (190°C). Grease a 9x13 inch baking dish.
Peel and slice potatoes into 1/4 inch thick slices. Place in a large bowl.
In a saucepan, melt butter over medium heat. Whisk in flour and cook for 1 minute.
Gradually whisk in milk until smooth. Bring to a simmer, stirring constantly.
Remove from heat and stir in 1.5 cups of cheddar cheese, salt, and pepper until cheese is melted.
Pour cheese sauce over potatoes and toss to coat. Pour potato mixture into prepared baking dish.
Sprinkle remaining 0.5 cup of cheddar cheese over the top.
Bake for 45 minutes, or until potatoes are tender and cheese is melted and bubbly.
Let stand for a few minutes before serving.