Cook the pasta al dente according to package directions. Before straining, reserve at least 1 cup of the pasta water and set aside.
In a large, heavy-bottomed pan over medium-high heat, add the sausage. Use a spatula or wooden spoon to break it into small crumbles.
When the sausage is about halfway cooked, add the red onion, bell pepper, and a pinch of kosher salt. Cook, stirring occasionally, until the vegetables begin to soften, about 5 minutes.
Stir in the garlic, red pepper flakes, and Italian seasoning. Cook for 2–3 more minutes, or until the garlic is soft and fragrant.
Add the balsamic vinegar to the pan and scrape up any brown bits from the bottom.
Pour in the crushed tomatoes. Then add ⅓ cup of water to the tomato can, swirl to collect the leftover juices, and pour that into the pan as well.
Let the sauce simmer for about 10 minutes, stirring occasionally, until slightly thickened. Stir in the balsamic glaze.
Taste and add more salt, black pepper, or additional balsamic glaze if desired.
Add the cooked rigatoni, grated Parmigiano-Reggiano, and a splash (about ¼ cup at a time) of reserved pasta water. Toss everything together until the pasta is well coated and the sauce is silky.
Top with slices or crumbles of goat cheese and a sprinkle of julienned fresh basil. Serve immediately