Preheat oven to 400°F.
Position oven racks in the top and bottom thirds of your oven. Line two large baking sheets with parchment paper.
Slice the potatoes using a mandoline into very thin slices. If you don't have a mandoline, slice them as thinly as possible with a sharp knife. Work in batches, slicing about half a potato at a time. Proceed to the next two steps till your first batch is coated in oil before beginning the next batch.
Pat the potato slices dry between sheets of paper towel. It may be tempting to skip this step - don't! It gives the chips their crispy texture.
Toss the potato slices in a bowl with 1/2 Tablespoon of each of the oils. Use your hands to rub the slices with the oil so each slice is coated. Arrange the slices in a single layer on a baking sheet. Sprinkle generously with salt.
Begin slicing the second batch of potatoes and continue till the second batch is on parchment paper.
When two sheets are full, bake until golden and crisp, switching the racks and rotating the pans halfway through baking time for a total of about 20 minutes. Small pieces may cook quickly, so remove them when they are done, leaving larger pieces to finish.
Remove to a plate and allow to cool. Continue with the next two batches.
Chips keep for one day. Store them in a paper bag or loosely wrapped in wax paper.
Enjoy with Leek Aïoli alongside burgers or mussels.