In a large skillet, heat 1 Tbsp. oil on medium-high heat. Cook sausage, stirring and breaking apart, until crumbled, about 5 minutes. Drain and transfer to a plate. Put 1 Tbsp. oil and onion in skillet; cook on medium heat, stirring often, until softened, about 4 minutes. Add to sausage and let cool.
Lower oven rack to bottom; preheat oven to 350°F. Line a baking sheet with parchment paper or foil; sprinkle with a little cornmeal or flour. Unroll dough onto pan without stretching. Sprinkle on 1 Tbsp. Parmesan. Spread sausage, onion and broccoli on top, pressing down slightly. Sprinkle remaining 1 Tbsp. Parmesan on top.
Bake until nicely browned on edges and cooked through, about 30 minutes. Cut into rectangles and serve warm or at room temperature.
