Preheat oven to 400 degrees. Lightly grease a 12-cup muffin tin. Using a mandoline, slice the potatoes into small rounds. In a large bowl, toss the potatoes, Parmesan, thyme, chives, sea salt, pepper and olive oil.
Generously fill each muffin opening to the top with a stack of potatoes. (Potatoes will shrink when baking.) Top the stacks with more Parmesan and sea salt if desired. Cover the pan with aluminum foil and roast for 35 minutes. Remove foil and roast for another 20 to 25 minutes until crisp and browned. Serve warm.