Trim and cut the broccoli into bite-sized pieces, cutting off the flowerets first and then cutting the larger ones in half or quarters.
In a sauté pan large enough to hold all the broccoli, sauté the garlic gently in a generous amount of oil, along with the peperoncino if using. When the garlic has turned a very light brown, remove it.
Add the broccoli pieces, turn them so they are entirely covered in the seasoned oil, seasoning well as you turn. Cover the pan and let the broccoli simmer until tender, turning from time to time—not too often or too vigorously, or you will smash the broccoli as it begins to get tender. The natural liquid of the broccoli will 'steam' the vegetable, but if things look dry, add a bit of water or white wine from time to time.
When the broccoli is tender, check and adjust for seasoning. Serve immediately.