Dissolve yeast in a cup of warm water. Add sugar and set aside for 25 minutes.
Sift all the flours and the potato starch into a large bowl and add 3 tablespoons olive oil and the sea salt. Gradually add the water with yeast, mixing well to form a soft dough. Turn the dough out onto a floured surface. Knead into an elastic dough, place back in the bowl, cover, and let sit to rise for 1 hour.
Preheat the oven to 410°F.
Line a baking sheet with parchment paper. When the dough has risen, roll it into a 10-inch diameter circle, around ¼-inch thick, dusting as needed. Place the pizza crust on the baking sheet. Spread the tomato sauce over the pizza crust, add sliced mushrooms, and transfer to the oven. Bake the pizza in the oven for 15 minutes, until golden-brown around the edges.
Remove from the oven. Add bell pepper, fresh tomatoes, and mixed greens. Season with pepper, drizzle with the remaining olive oil, and serve.