Chop fresh broccoli into small florets. If using frozen, let it stand out a few minutes, then give it a quick coarse chop. Measure and set aside.
Set a large colander in the sink with a glass mug in the center of the colander (so you don’t forget to grab some pasta water before draining!). Bring a large pot of water to a boil. Generously salt the water (I add 2 teaspoons salt), then cook pasta according to package instructions—minus 1 minute. Two minutes before draining time, add broccoli. Right before draining, use mug to remove a big scoop of pasta water (set aside) and drain the pasta. Don’t rinse under cool water.
Meanwhile, in a large pan (that will need to fit the pasta and broccoli), heat the butter. Once melted, add garlic and all seasonings. Season with salt and pepper (I add 1/4 teaspoon each) Cook until golden, stirring constantly, about 30 seconds. Pour in 1/2 cup chicken broth; it should sizzle and boil. Scrape up any browned bits off the pan. Once this broth mostly evaporates, add the other 1/2 cup. Stir.
Add in heavy cream and Parmesan cheese. Stir to mix. Simmer over medium heat, stirring occasionally, 3–5 minutes or until sauce thickens and slightly reduces. The sauce shouldn’t boil—reduce heat and stir more frequently if needed.
Once you have a thick and creamy sauce, add drained pasta and broccoli. Use tongs to toss ingredients into cream sauce until sauce thickens and nicely coats the pasta, 1–2 minutes. If sauce is too thick, slowly add in set-aside pasta water. Taste and adjust, adding more salt/pepper to taste. Add lemon zest to taste if desired.
Serve immediately. Top individual plates with a touch more Parmesan if you like and fresh parsley. Add red pepper flakes and a squeeze of fresh lemon juice to individual plates as desired. Enjoy immediately! Pasta is best enjoyed right after being tossed!
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Notes
Note 1: Grab a block of Parmesan and grate it on the small holes of a grater. Alternatively use finely grated Parmesan cheese. Parmesan from a can will be too salty and won’t melt into the sauce nicely.Storage: Store leftovers in the fridge in an airtight container for up to 3 days. Reheat on the stove or in the microwave, adding a little broth or cream if the sauce is too thick.