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Heat a large pot or Dutch oven over medium-high heat. Add butter and onion and let cook for 5-6 minutes, stirring often. Add garlic and cook for 30 seconds. Meanwhile, peel and slice potatoes.
Add heavy cream, milk, thyme, salt, pepper, and potatoes. Cover with a lid and reduce heat to low to keep a mild simmer. Parboil potatoes for about 15 minutes, or until the potatoes are almost tender. Preheat oven to 350 degrees.
Transfer potato mixture to 3-quart baking dish or gratin dish. Sprinkle with cheddar cheese. If you want the cheese to be melted throughout, carefully mix the cheese into the potatoes.
Bake until bubbling around the edges and cheese is melted and golden, about 20-25 minutes. Let cool for 5 minutes before serving.