Preheat oven to 375°F.
In a small bowl, combine butter and oil.
With a sharp knife or mandoline, slice potatoes crosswise very thinly.
Choose a baking dish and pour a tablespoon of the butter/oil mixture in the bottom, spreading it evenly.
Sprinkle the oil mixture with a few pinches of coarse salt and red pepper flakes, if using.
Arrange potato slices vertically in the dish.
Thinly slice shallots and slide shallot slivers between potato wedges, distributing them evenly.
Brush with remaining oil/butter mixture and generously season with salt.
Bake for 1 ¼ hours, then arrange thyme sprigs on top and bake for an additional 35 minutes until cooked through with a crisped top.
If browning too fast, cover with foil.
Add any garnishes, if using, and serve immediately.
