Cook potato in boiling water to cover 5 minutes; drain.
Layer one-third potato slices, one-third onion slices, and one-third cheese slices in a lightly greased 13- x 9-inch baking dish.
Sprinkle with 1/4 teaspoon salt and 1/4 teaspoon pepper. Repeat layers twice with remaining potato, onion, cheese slices, salt, and pepper. Top with Cheddar cheese.
Melt butter in a heavy saucepan over low heat; add flour, whisking until smooth. Cook, whisking constantly, 1 minute. Gradually whisk in milk until smooth.