Preheat the oven to 425°F. Line a large baking sheet with parchment paper (use a baking sheet that will fit both of the flatbreads without them overlapping).
In a large skillet over medium heat, sauté the broccoli and onions, stirring frequently, until they begin to soften, 2 to 3 minutes.
Add the garlic and sauté for another minute, stirring constantly (turn down the heat, if needed, so that the broccoli doesn't burn).
Turn off the heat, taste the mixture, and season to taste with salt and pepper.
Place the flatbreads on the baking sheet. On each flatbread, spread 2 tablespoons of the ricotta cheese, leaving about a ½-inch border around the edges.
Top each flatbread with 2 tablespoons of the Parmesan cheese, ½ cup of the mozzarella cheese, half of the broccoli mixture, and 2 more tablespoons of mozzarella cheese.
Bake for 12 to 15 minutes in the middle of the oven until the cheese is melted and bubbly and the flatbread is golden brown and crisp around the edges.
Cut each pizza into 4 slices; serve immediately.