2 tablespoons extra-virgin olive oil
4 fleshy red bell peppers, seeded and cut into strips
1 medium-sized onion, thinly sliced and separated into rings
2 large cloves garlic, finely chopped
1 bunch fresh broccoli (about 1 pound), broken into florets and stems cut into 1/2-inch pieces
Salt and freshly-ground black pepper to taste
Grated cheese (optional)
In a large skillet, heat the olive oil over medium heat. Cook the red peppers, onion, and garlic until soft, adding small amounts of water to keep the skillet from drying out and stirring from time to time, about 30 minutes.
Meanwhile, bring a saucepan of water to a boil, salt lightly, and cook broccoli stems for a few minutes, then add florets. Cook broccoli until tender but still bright green, no more than about 10 minutes. Drain, break up slightly with a fork, and toss with the red bell pepper mixture. Season with salt and pepper, top with grated cheese, if desired, and serve immediately.