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1
Add the dried spaghetti to a 12-inch skillet or saute pan (or a 10-inch will work fine if that's what you've got), and cover the noodles fully with water, filling the skillet about two-thirds of the way total. Add several large pinches of salt. Set over a medium flame. (Cooking the pasta this way yields much starchier water, which'll help thicken our sauce later.)
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2
While the pasta water heats, brown the sausage: In a separate large pot (big enough to hold all of the pasta, eventually), heat 2 tablespoons olive oil over a medium-high flame until very hot and glistening. Add the uncased sausage and brown thoroughly on one side without jostling, about 3 to 4 minutes. Use a slotted or wooden spoon to break the sausage into small, bite-sized pieces as you flip to brown its other side thoroughly. Once fully browned and cooked through, use a slotted spoon to move the sausage to a separate plate off heat.
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3
Check on your pasta. When the water has come to a boil, you want to let it go for about 2 to 3 minutes, until the noodles are pliable but still quite al dente (you'll be cooking them for another 2 minutes later, in the sauce, and letting them hang out in the hot water in the meantime, which will cook them more). Turn off the heat.
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4
Meanwhile, back in the big pot, drain about half of the sausage fat and oil, then add another 2 tablespoons of olive oil over a medium-low flame. (This will give the final dish a subtle-but not overwhelming-sausage flavor.) Don't worry about any straggler fennel seeds that have fallen out of the sausage pieces, into the oil. Add the garlic and saute about 3 minutes, until fragrant and just starting to toast. Add the red chili flakes and saute another 30 seconds. Use a measuring cup to transfer 2 1/4 cups of the starchy pasta cooking water from the skillet to the pot of garlic and red chili flakes. Scrape up any browned bits from the bottom of the pot and turn heat to medium-high to bring the water to a rolling simmer. Reduce by about one-half, which will take roughly 4 to 5 minutes. Turn the flame down to low.
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5
Then, using tongs or two slotted spoons (or, if you're me, some precarious combination of forks), transfer over the spaghetti from the skillet of water into the pot with the reduced sauce. Add the grated Parmesan, parsley, sausage pieces, and salt. Toss together over the low flame until the cheese melts and an emulsified sauce coats all of the noodles. Taste and add more salt if needed. Serve immediately while hot, garnished with more grated Parmesan and chopped parsley.
