Heat oven to 375°F. Combine butter and oil in a small bowl. Brush the bottom of a small round baking dish (or two individual baking dishes) with some of the butter mixture and set aside.

Using a mandoline or very sharp knife, slice potatoes very thinly crosswise. The thinner the potato, the crispier it will get in the oven. Vertically arrange potato slices in the baking dish(es) and wedge shallots throughout. Sprinkle with red pepper flakes and salt. Brush tops with remaining butter mixture.

Bake for 1 hour; then add fresh time and bake for an additional 35 minutes or until potatoes are tender and cooked through and tops are crispy.