Preheat oven to 400°F (200°C). Line an 8-cup muffin tin with squares of foil coated with cooking spray. Foil should extend over muffin cup to edges to create handles. Set aside.
In a small skillet, add oil and shallots and cook over medium heat until tender but not browned, about 2 min. Remove from heat and cool completely.
In a bowl, combine potato with shallots, thyme, salt and pepper until well coated. In another bowl, combine cheddar and Parmesan.
Place a layer of potato slices in the bottom of each muffin cup. Sprinkle a heaping teaspoon of cheese mixture into each cup. Repeat layers (gently pressing potatoes to pack down) until all ingredients are used up and muffin cups are filled, finishing with cheese mixture on top.
Bake on middle rack of oven until tops are golden and potatoes are tender when pierced with a fork, about 40 min. Let rest 10 min. before lifting out with foil handles and gently pulling away the foil with the tip of a knife (watch out for steam). Serve immediately.
We used an 8-cup muffin tin to create individual portions. You can also use a 12-cup muffin tin for smaller galettes or a 13 × 9-in. (3 L) baking dish for a family style feel – just increase the bake time by 10 min.