1lb.broccolinicut into 1/2" pieces, (or broccoli, fresh or frozen, or broccoli rabe)
grated parmesan, chopped parsley, and fresh cracked black pepperfor serving (optional)
Add the sausage (1 lb.) and onions to a large, deep skillet, pot, or Dutch Oven with a lid(make sure it's big enough to add the pasta in later!). Cook over medium high heat until the sausage has browned and the onions have softened, breaking up the sausage with a wooden spoon as it cooks, about 5 minutes.
Turn the heat down to medium and add the minced garlic (2 cloves) and crushed red pepper (1/4 teaspoon) if using. Sauté for 1-2 minutes, until garlic is fragrant. If you find that some of the sausage has stuck to the bottom of the pan, add 2-4 tablespoons of water, chicken broth, or white wine to the skillet, using a wooden spoon to help dislodge any stuck-on bits.
Add chicken broth (2.5 cups) and bring to a boil. Add the pasta, along with 1/2 teaspoon kosher salt (if using water, use 1 full teaspoon, and if using a chicken broth with lots of sodium, omit entirely).
Stir, turn heat down to low, cover, and simmer for 12 minutes (at this point, the pasta won't be entirely cooked yet). Add the broccoli, stir, cover, and simmer for another 3-5 minutes, until pasta is fully cooked and broccoli has softened and turned a bright green. (If it seems a little "soupy" but the pasta is fully cooked, I recommend letting it sit uncovered for 5-10 minutes to allow it to cool, thicken, and the steam to evaporate a bit.)
Serve with fresh grated parmesan cheese, chopped parsley, fresh cracked black pepper, and a little more crushed red pepper if desired.
You can save time by making this traditionally, without one pot. One pot pastas save on dishes and steps but take a little longer. You can cook the pasta separately in heavily salted water until 1 minute before al dente. While the pasta is cooking, sauté the sausage, onions, garlic, and crushed red pepper as directed. When the pasta is done, use a slotted spoon to transfer it to the skillet along with the broccoli and 1/2 cup pasta water. Let it cook for another 3-4 minutes until the sauce has thickened, the broccoli has softened, and the pasta has finished cooking.
If using broccoli rabe, it will likely take less cooking time, so add it in after 14 minutes and let it cook only for another 1-2 minutes.
If using broccoli, follow the same instructions as for broccolini. If using frozen broccoli, add it 1 minute sooner.