1. Preheat oven to 475ºF. Warm 1 Tbsp. oil in a skillet over medium-high heat. Add mushrooms, sprinkle with salt and sauté until mushrooms release their liquid and are lightly browned, 5 to 7 minutes. Transfer to a small bowl.
2. Press and stretch dough evenly to cover a 15-inch round perforated pizza pan. Scatter mushrooms over dough; sprinkle cheese on top. Bake until underside is golden and cheese is bubbling, about 15 minutes.
3. Toss arugula with remaining 1 Tbsp. olive oil, lemon juice and 1/2 tsp. salt. Arrange greens on top of pizza. Scatter tomatoes over greens. Return pizza to oven to wilt arugula, 2 to 3 minutes. Slice and serve.