Preheat your oven to 400° and line a baking sheet with parchment paper.
Thinly slice the potatoes. If you have a mandolin or a slicing blade for your food processor, it will work great for this. If not, carefully cut the potatoes into slices that are about 1/4” thick with a sharp knife.
In a medium bowl, toss the potato slices in 1 teaspoon of oil, 1/2 teaspoon of sea salt, and the black pepper. Line the slices on the prepared baking sheet so that none are overlapping, and bake for 10 minutes, until they brown slightly.
While the potatoes are cooking, heat the remaining oil a medium-sized pan over medium-high heat. Add the mushrooms and the rest of the salt, and cook until the mushrooms brown and release their liquid, about 10 minutes.
To make the pizza, spread the pesto over the crust, leaving about an inch around the edges. Layer the potato slices on top of the pesto, then add the mushrooms, olives, and the red pepper flakes. Bake for 10 – 15 minutes, until the crust is golden brown.
Remove the pizza from the oven and top with the arugula. Slice and serve hot.