Heat oven to 375 F.
In a small bowl, combine butter and oil. Brush bottom of a 9-inch round baking dish or cast iron skillet.
With a sharp knife or mandoline, slice potatoes very thinly crosswise.
Arrange potato slices vertically in the baking dish. Wedge sliced shallots throughout. Sprinkle with salt and red pepper flakes. Add thyme sprigs and brush with remaining butter mixture.
Bake for 1 ¼ hours until potatoes are fork tender and crispy on top. Sprinkle with additional thyme to serve, if desired.