Heat oven to 375 degrees. In a saucepan over low heat, combine cream, stock, thyme, garlic, and nutmeg. Simmer about 5 minutes; then let cool about 10 minutes. Strain and discard garlic and thyme.

Butter a 9x13-inch casserole dish. Place a layer of potatoes in an overlapping pattern and season with salt and pepper. Pour a third of the cream over potatoes. Top with 2 tablespoons Parmesan cheese. Repeat for two more layers.

Bake, uncovered, 45 minutes. Sprinkle remaining cheese on top and place under broiler until cheese browns, about 5 minutes.