- Bring a stockpot of water to a boil and salt it. Trim the broccoli and cut it into pieces. Add the broccoli to the pot and return the water to a boil.
- Meanwhile, put the oil in a large skillet over medium-low heat. When the oil is hot, add the garlic and the sausage. Cook, stirring occasionally, until the garlic is fragrant and the sausage is well browned, about 5 minutes. Remove it from the skillet and turn the heat off.
- Start checking the broccoli after 5 minutes. You want it fully tender but not mushy; this could take up to 10 minutes. Use a slotted spoon or small strainer to scoop up the broccoli, drain excess water, and transfer it to the skillet (keep the water boiling).
- Cook the broccoli over medium-high heat, stirring and mashing it slightly with a potato masher until it is quite soft and breaks apart. If you need to, add a tablespoon or two of the boiling water to help soften the broccoli. Meanwhile, cook the pasta in the boiling water until it is tender but not mushy; start tasting after 5 minutes.
- When the pasta is done, scoop out and reserve at least 1 cup of the cooking water, then drain it. Add the pasta, sausage, and a splash of the cooking water to the broccoli; toss until combined, adding a little more water or olive oil if necessary to make a slightly creamy sauce. Taste and adjust the seasoning, adding lots of black pepper and parmesan cheese. Toss again and serve, passing more cheese at the table.
Note: Don’t skimp on the olive oil since it adds body and flavor to the sauce. In fact, I add another tablespoon or two when tossing the pasta for richness, moisture, and flavor.