Preheat oven to 425°F with a pizza stone on the bottom rack if you have one (you want the pizza stone to heat up with the oven).

Heat 2 tablespoons olive oil in a large, non-stick skillet over medium-high heat. Add shallot, garlic, and red pepper flakes and cook for 2-3 minutes, stirring occasionally, until the shallot begins to soften. Add mushrooms and salt and cook, stirring occasionally, until the mushrooms are well browned, about 7-10 minutes.

Place pizza crust on top of a pizza peel or wooden cutting board. Top crust with mushroom mixture and spread evenly, leaving a 1-inch border around the outer edges. Dot with ricotta and sprinkle Parmesan and chives over top.

Transfer pizza to the preheated pizza stone (or a baking sheet, if you're using that instead) and bake for 5-6 minutes (8-9 minutes without the pizza stone).

Remove pizza from oven and transfer to a cutting board. Scatter wild arugula over top and drizzle with aged balsamic and olive oil. Cut into slices and enjoy!