Heat oven to 400 degrees. In a small bowl, combine butter and oil. Brush the bottom of a round 9-inch baking dish with butter mixture. Using a mandolin, slice potatoes crosswise very thinly.
Arrange potatoes thin sides up in dish slightly fanning out slices as you go. Wedge shallot slices sporadically throughout. Sprinkle pepper flakes over potatoes, season generously with salt and 1/4 teaspoon pepper and brush with remaining butter mixture. Roast until potatoes are cooked through, with a golden-crisp crust, about 1 hour. Tuck remaining thyme around potatoes and bake for 15 minutes more.
