Preheat the oven to 475 degrees F. If using frozen broccoli, thaw it according to the directions on the package.
Finely grate the parmesan, then place 1/3 cup into the bowl of a food processor along with the broccoli, 2/3 cup basil, 1/4 teaspoon salt and 1/4 teaspoon pepper. While the processor is running, drizzle in 3 tablespoons olive oil. Process until smooth, scraping down the sides of the bowl as needed.
Sprinkle a work surface with the cornmeal and use a rolling pin and/or your hands to stretch the dough into a 12-inch circle. Spray the baking sheet with cooking spray and place the dough onto it. Spread the broccoli pesto over the dough, leaving a border for the crust. Scatter the goat cheese over the top of the pesto, then thinly slice the tomato and arrange the slices on top.
Bake until the cheese and tomatoes are softened and the crust is golden brown, 12 to 14 minutes.
Garnish the pizza with the remaining parmesan, the remaining 1/3 cup basil and the red pepper flakes. Drizzle with the remaining 2 teaspoons olive oil and slice the pizza into 8 wedges.