Cut Yukon Gold and sweet potatoes into 1/8 inch slices; toss with oil and sprinkle with salt and pepper. Divide between two greased 15x10 inch baking sheets. Roast at 425 for 17 to 20 minutes or until tender.
Meanwhile, in a small saucepan, melt butter. Add garlic and thyme; cook and stir for a minute. Put roasted potatoes in a large bowl. Add butter mixture; toss to coat. Sprinkle with cheeses; toss to combine.
You can serve in a bowl or you can layer the slices on a platter or plate, by placing potatoes gold then sweet, top with fresh thyme.