Preheat your oven to 375 degrees Fahrenheit.
Using a mandoline slicer or a sharp knife, slice the sweet potatoes, red potatoes, and purple potatoes into slices about 1/8 inch thick. Try to make the slices as even as possible, and choose potatoes with approximately the same circumference. You should end up with approximately 100-120 slices, depending on thickness.
Add the potato slices to a large bowl and toss well with the olive oil, rosemary, thyme, garlic, sea salt, and pepper until the potatoes are evenly coated.
Arrange the potato slices in your choice of casserole or baking dish (approximately 9-inch by 13-inch in size, preferably oval or round in shape) in a spiral pattern, alternating sweet, red and then purple slices to create a patterned design (if you wish).
If there is any leftover oil and herb mixture, pour it evenly over the potatoes you've arranges in the baking dish.
Bake, uncovered, for about 30-35 minutes, or just until the potatoes are fork tender.
Serve immediately, with some shaved parmesan on top if desired.