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Trim off the ends of each Brussels sprout, remove any discolored or loose leaves, and cut into quarters. Set aside.
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Fill a stock pot with water. Turn heat to high and boil water.
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Place a 10 – 12-inch skillet on a burner and turn it on to medium high heat. Add the olive oil. When the olive oil is hot and shiny, add the sausage. Cook the sausage until it is no longer pink and completely cooked through. Use a wooden spoon, or fork, to stir the sausage and break it into crumbly chunks. When just cooked through, turn off the heat and remove the sausage from the pan using a slotted spoon. Set the sausage aside on a plate, or in a bowl.
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Meanwhile, when the water comes to a boil add 1 teaspoon of Kosher salt and the pasta. Cook according to the directions on the back of the box, making sure the pasta is al dente when finished. Frequently stir the pasta to prevent the pasta from sticking together.
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Turn the heat back on and add the minced garlic, red pepper flakes, and crushed fennel. Cook briefly until you begin to smell the garlic then add the Brussels sprouts and ½ teaspoon of Kosher salt. Stir to mix the Brussels sprouts with the garlic and red pepper flakes, then allow the Brussels sprouts to cook through and get golden brown on the sides. Add extra olive oil if the pan if it is dry.
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Add the vegetable stock, chicken stock, or water to the pan then stir to combine. Cover the skillet with a fitted lid, and cook the Brussels sprouts until they become soft but still bright green, about 4 minutes.
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Uncover the pot and turn off the heat if the pasta is not ready.
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Once the pasta is done, collect about ½ cup of the pasta water, then drain the pasta. Add the cooked pasta back into the stock pot then add the sausage and Brussels sprouts. Stir to evenly combine then add the parsley, lemon zest, fresh fennel fronds if using, about 3 Tb of pasta water, and butter. Gently stir to combine.
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Serve immediately while hot with grated Romano or Parmesan Reggiano cheese.