Preheat the oven to 350 degrees F. Butter an 8-by-8-inch baking dish.
Whisk together the half-and-half, salt and pepper in a large bowl or liquid measure with a spout. Toss together the Havarti, Gouda and 3/4 cup of the Cheddar in a small bowl.
Slightly overlap a third of the potato slices on the bottom of the baking dish. Sprinkle with a third of the cheese mixture and pour a third of the half-and-half mixture over the top. Repeat for 2 more layers with the remaining potatoes, cheese mixture and half-and-half mixture. Sprinkle the remaining 1/2 cup Cheddar over the top.
Bake until the potatoes pierce easily with a knife and the top is golden, 1 hour 20 minutes to 1 hour 30 minutes. Let rest for 10 minutes before serving.