Separate the broccoli florets from the stalks. With a vegetable peeler or a small, sharp knife, remove the coarse outer layer of the stalks to reveal the pale green, tender heart. Cut the stalks into 1 cm lengths. Cut the florets into pieces approximately the same size as the stems, but keep them separate. You should have about 1 pound of broccoli after trimming.
Heat the olive oil in a large skillet over moderately low heat. Add the garlic and saute until fragrant, about 1 minute. Add the hot pepper flakes (use the full quarter teaspoon if you want it really peppery), broccoli stems, and 1 tablespoon of chicken stock. Cover and cook until the broccoli stems are almost tender, about 5-7 minutes; add a bit more stock if necessary to keep the stems from sticking. Add the florets and the remaining tablespoon of stock; cover and cook until tender, about 5 minutes, shaking the skillet occasionally so that the broccoli cooks evenly.
Transfer the broccoli to a warm serving bowl; sprinkle with cheese and salt to taste (be careful; the cheese is salty). Toss again, then serve.