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Step 1
Trim off the bottom 2-3 inches of the broccoli stems, depending on how dry or fibrous they are (disgard or add to your compost). Slice off and separate the green stem from the florets. Cut the stem into approximately 1-inch pieces, and break or slice the florets into bite-size pieces.
Step 2
Bring 4-6 quarts of water to a boil in a large pot. Add 2-3 tablespoons kosher salt, until it tastes pleasantly salty — this helps to season the broccoli and pasta from the inside out.
Step 3
Drop the broccoli pieces into the boiling water and cook for one minute. Scoop the broccoli out with a slotted spoon, transferring it into a colander set over a bowl to help it drain. Scoop out 1 cup of the boiling water into a small bowl. Keep the pot covered on a low boil until you're ready to cook the pasta.
Step 4
Add the olive oil, garlic and red pepper to a skillet or saute pan that's large enough to hold the broccoli and sauce, 10-12-inches in diameter. Cook over medium-high heat until the garlic smells fragrant, 1-2 minutes, but don't brown it. Stir in the broccoli, ½ teaspoon salt and the reserved cup of water.
Step 5
Cover the pan, reduce the heat to medium and cook 15-20 minutes. The broccoli should be soft enough to squish with a spatula. Mash some of the pieces against the side of the pan to make a creamier sauce.
Step 6
Meanwhile, cook the pasta until al dente, following the package directions. Scoop out and reserve ½ cup of the pasta cooking water. Drain the pasta and add to the skillet with the grated Parmesan, parsley and lemon zest. Stir until the pasta is coated with the sauce (you can dribble in some of the pasta water a tablespoon at a time if the sauce looks dry). Serve right away, with more Parmesan cheese sprinkled over.