Bring a large pot of well-salted water to a boil.
Heat the oil in a 12-inch skillet over medium-high heat. Add the sausage and cook, turning often, until cooked through, 6 to 8 minutes. Transfer to a cutting board.
Add the onion, fennel, garlic, and 1/2 tsp. salt to the skillet. Stir, cover, turn the heat down to medium low, and cook, stirring occasionally, until tender and starting to brown, about 5 minutes.
Meanwhile, cook the pasta according to package directions until al dente. Reserve 2 cups of the pasta water, drain the pasta, and return to it the pot, off the heat. Cover while finishing the sauce.
Uncover the skillet and add the sun-dried tomatoes, red pepper flakes, another 1/2 tsp. salt, 1/2 tsp. pepper, and 1 cup of the reserved pasta water. Turn the heat up to medium high and cook, stirring, for 5 minutes.
Slice the sausage 1/4 inch thick. Add the sausage, half the cheese, and the remaining 1 cup of pasta water to the skillet and cook until the sauce thickens somewhat, about 5 minutes. Toss the sauce, parsley, and the remaining cheese with the pasta. Season to taste with salt and pepper and serve immediately.