Bring a large pot of water to a boil.While the water is
heating, cut the florets off the broccoli. Peel the stems and cut them into rather thick slices, about 1⁄3 inch. When the water comes to a boil, add the broccoli and cover the pot to bring it back to a boil quickly. Blanch the broccoli for 5 minutes. Drain.
Put olive oil and garlic into a large skillet over medium heat. When the garlic starts to sizzle, add the hot peppers and anchovies. Cook, giving a stir or two, until the anchovies melt. Add the broccoli, season with salt and pepper, and stir well. Cover the skillet, turn the heat to very low, and cook for 2 hours. Use a spatula to turn the broccoli over in the skillet a few times, but try not to break it up. It will be very tender when done.
Use a slotted spoon to transfer the broccoli to a serving dish. It is delicious hot or at room temperature.
Recipe Notes
*Finamore likes small fresh red peppers, but you can substitute green Thai chiles, various dried ones, even a big pinch of red chile flakes.