How to Make It
In a large deep frying pan, heat the oil over moderately low heat. Add the garlic and broccoli stems and cook, stirring occasionally, for 2 minutes. Add the broccoli florets, 1/2 teaspoon of the salt, and the pepper. Stir to coat with the oil.
Add the tomatoes and broth to the broccoli and bring to a simmer. Reduce the heat and simmer, covered, until the broccoli is tender, 5 to 10 minutes.
Meanwhile, in a large pot of boiling, salted water, cook the orecchiette until done, about 15 minutes. Drain the pasta and add it to the pan with the broccoli. Remove the pan from the heat. Add the vinegar, the remaining 1/2 teaspoon salt, the parsley, and butter. Stir gently until the butter just coats the pasta.
Broccoli stems are a delicious vegetable in their own right. Peel the thick skin and then slice or cut the stems into pieces. If you're cooking them with the florets, either cut the stems into quite small pieces so they'll be done at the same time, or cook them for a few minutes before adding the florets.