In a medium bowl, combine the basil, 1/2 cup of the olive oil, the salt and tomato puree. Stir together until combined. Cover with plastic wrap and refrigerate for at least 3 hours to allow the flavors to marry.
Preheat the oven to 500 degrees F. Place a rack on the highest level and leave space on the bottom of the oven for easy access.
Heat a large skillet over high heat. Add the remaining 2 tablespoons olive oil and the sausage and cook, breaking apart with a wooden spoon to form bite-size pieces, until golden brown and cooked through, about 10 minutes. Add the broccoli to the pan and stir to mix with the sausage. Remove from the heat and cool to room temperature.
Dust an upside-down rimmed baking sheet with the flour. Gently stretch the pizza dough and place on the dusted tray. Continue to stretch out to 1/4-inch thick leaving it a little thicker around the edges. Spread 1 cup of the sauce over the dough and top with the mozzarella. Spread the sausage and broccoli evenly over the crust and top with the Parmesan. Place the sheet tray directly on the bottom of the oven and bake for 5 minutes. Move the tray to the top shelf and finish cooking until golden brown and the crust is cooked, 5 minutes.