Preheat oven to 425°F. Roll dough out to 12-inch square on an unfloured work surface. Sprinkle large baking sheet with cornmeal and place dough on top. Sprinkle Parmesan over dough. Bake until Parmesan starts to brown and pizza begins to puff, about 15 minutes.
Meanwhile, in large mixing bowl, whisk together vinegar, mustard, brown sugar, and salt. Add tomatoes and onion, and toss to combine. Set aside.
Top pizza with mozzarella and return to oven. Bake until cheese has melted and pizza bottom is crisp, about 5 minutes.
Add salad greens to tomato mixture and toss to coat. Scatter salad over hot pizza and serve.