Preheat the oven to 375 degrees F. Melt the butter in a large pot over medium-high heat. Add the onions and saute until softened and beginning to brown. Add the garlic and continue cooking 1 minute longer. Stir in the cream, broth and thyme, and season with the salt and pepper. Add the potatoes and bring to a simmer. Continue cooking until the potatoes are fork-tender, 10 to 15 minutes.
Transfer the potatoes and cream to a shallow baking dish. Sprinkle the cheeses evenly over the potatoes. Bake until bubbly and the surface begins to brown, 15 to 20 minutes. Let sit 10 minutes before serving.