Rinse and drain the broccoli head and cut apart all the main branches where they join or are attached to a central stem. Separate the clusters into medium size florets, 2 to 3 inches wide at the top. If they are wider, slice them lengthwise. Cut their long stems so the florets are about 4-inches long.
Peel the tough skin from the stem pieces and slice them lengthwise in half or in quarters if they are thick. You can also peel or slice off the tough fibrous layer of the large branches and central stems and slice up the fresh core into 4-inch sticks. Discard all dry and hard pieces.
Set the skillet over moderate heat, pour in the oil and strew in the garlic. Cook the slices for about 5 minutes, with an occasional shake. When they’re lightly caramelized, dump the broccoli pieces into the skillet, sprinkle the salt and peperoncino all around and pour in the water.
Cover the pan, raise the heat slightly and cook for 5 minutes, shaking the pan a couple of times. Lift the cover and toss everything very well then cover again.
Let the broccoli cook another 3 to 5 minutes, and poke or taste a piece to check the tenderness. Cook longer, covered, if you want it softer. Remove from the heat and uncover the pan as soon as the broccoli is cooked through and still brightly colored. Serve right away.