In a large skillet (preferably one with a lid), warm olive oil over medium heat until hot. Carefully add onion, garlic and salt, and sauté, stirring often, until onion becomes transparent and garlic just begins to turn golden brown, 4 to 5 minutes.
Toss in broccoli; sauté for 3 minutes. Add chickpeas, broth and red pepper. Stir once, cover and cook for 3 minutes more, just to heat through and finish cooking broccoli.
Uncover, season with pepper, sprinkle with Parmesan and serve.