Preheat oven to 375 degrees. Butter large baking dish. Slice potatoes 1/4 inch thick.
In a large skillet over medium heat, melt butter. Add garlic and cook about 1 minute. Add cream, milk, thyme, nutmeg, salt, and red pepper flakes. Bring to boil and reduce heat to low. Let simmer 10 minutes. Remove from heat.
Layer 1/3 of sliced potatoes, slightly overlapping, in prepared dish then pour 1/3 of cream mixture over potatoes. Repeat with remaining potatoes and cream to make two more layers. Cover with Swiss Cheese on top.
Cover with foil and bake for 45 minutes. Uncover, sprinkle with Parmesan and continue baking until potatoes are tender and golden (about 15 to 20 minutes).