Start a large pot of water so it’s close to boiling by the time you begin the sauce.

Heat the olive oil in a large, deep skillet or saute pan over medium heat. Add the sausage and cook for about 4–5 minutes until browned. Stir frequently while breaking up large pieces with a wooden spoon or spatula.

Lower the heat to medium-low and add the garlic. Cook for 1 minute, stirring often.

Add the butter to the skillet. Once it melts, add the flour and mix well. Cook for 2–2½ minutes, stirring almost constantly.

Slowly add the milk to the skillet while stirring and gently scraping up any browned bits from the bottom of the pan. Continue stirring until the ingredients are combined.

When the sauce comes to a simmer, cover and cook for 10 minutes, stirring occasionally. Keep it at a gentle simmer; if it starts to boil too vigorously, reduce the heat.

While the sauce cooks, drop the pasta into the boiling water. Cook according to package directions for al dente. Remember to salt the water and stir occasionally.

Before draining the pasta, reserve about 1 cup of the cooking water to use later in the sauce. Drain the pasta.

While the pasta and sauce are cooking, make the frozen broccoli according to package directions. (I use the lowest cooking time listed on the package, minus one minute.) Drain the broccoli well.

While the pasta is still hot and steaming, add it to the creamy sauce along with about ¼ cup of the reserved pasta water and the broccoli. Stir well until the ingredients are combined and coated. If the sauce is too thick, add a little more of the reserved pasta water and stir again.

Stir in the Parmesan cheese. Taste and add salt, if needed. (As a reference, we added about ½ teaspoon to ours.)

Serve immediately with crushed red pepper and extra Parmesan cheese, if desired.