Cut stalks off the broccoli, and peel off the coarse fibrous skin using vegetable peeler. Dice stalks into ½-inch pieces, cut florets into ½-inch pieces, and set aside.
Heat olive oil in a large skillet over medium-high heat. Add onion and garlic, and cook until softened, about 4 minutes. Add chopped broccoli stalks and cook until stalks soften, about 3 minutes, tossing pan regularly to avoid any over-browning. Add broccoli florets, continuing to sauté until tender and bright green. Season with salt, pepper and cayenne. Serve hot.
Yields 6 servings