Preheat oven to 450°F. In a large bowl, combine potatoes, oil, paprika, salt, pepper, cayenne and thyme; toss well to coat.
Divide potatoes between 2 rimmed baking sheets, spreading in a single layer. Bake for 20 minutes. Remove pans from oven and flip potatoes over. Sprinkle with garlic. Return pans to oven and bake 20 minutes longer.
Serve potatoes hot or at room temperature.