Fill a large pot with water, add a pinch of salt, and bring to a rolling boil over high heat.
Add 1 pound corkscrew pasta (rotini) and cook until al dente according to package directions; before draining, scoop out and reserve 1 cup of pasta water, then drain and set the pasta aside.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add 1 pound Italian sausage, casings removed, and break it up with a spoon; cook until browned and no longer pink, about 5–7 minutes, ensuring it reaches 160°F internally; transfer the sausage to a plate, leaving the rendered fat in the skillet.
Reduce heat to medium; add 1 large chopped onion and 2 chopped bell peppers and sauté until softened, about 5–7 minutes.
Stir in 3 cloves minced garlic and cook until fragrant, about 1 minute.
Pour in 1 can (28-ounce) crushed tomatoes and 0.5 cup chicken broth; season with 0.5 teaspoon salt and 0.25 teaspoon black pepper; bring to a gentle simmer, then reduce heat to low, cover, and cook for 10 minutes, adding reserved pasta water if needed to thin the sauce.
Return the cooked pasta and browned sausage to the skillet; stir in 0.5 cup grated Parmesan cheese and 0.25 cup fresh chopped basil; toss until the pasta is well coated and heated through, then taste and adjust seasonings.
Serve immediately, topped with extra grated Parmesan cheese and a sprinkle of fresh basil.