Heat the oven to 375°F and grease a 9-by-13-inch dish. Melt butter, add flour for 1 minute, then whisk in milk, thyme, salt and pepper until thickened.

Remove from heat and stir in 2 1/2 cups Gruyère.

Layer one-third potatoes, half the ham and one-third sauce. Repeat, then finish with remaining potatoes and sauce.

Cover tightly and bake for 55 minutes. Uncover, add remaining Gruyère and bake 15 to 20 minutes more until tender and browned.

Rest 15 minutes before cutting.