Brown the sausage: Set a large pot or Dutch oven over medium-high heat.
Add the sausage and cook, breaking it into small pieces, until browned and cooked through, 6–8 minutes. If there’s excess fat, spoon off all but about 1 tablespoon.
Sauté the aromatics: Add onion, carrots, and celery. Cook, stirring, until softened and lightly golden, about 5–7 minutes.
Add garlic, oregano, thyme, and red pepper flakes; cook until fragrant, about 30 seconds.
Build the base: Stir in the tomato paste and cook for 1 minute to caramelize. Add the diced tomatoes with their juices and the chicken broth. Scrape up any browned bits from the bottom—those add big flavor.
Simmer the soup: Bring to a boil, then reduce to a steady simmer.
Cook for 10–12 minutes to let the flavors meld.
Add the pasta: Stir in the pasta. Simmer until just al dente, checking package timing and starting to test a minute early. Stir occasionally so the pasta doesn’t stick to the bottom.
Finish with greens and cream: Add the chopped greens and cook until wilted and tender, 2–4 minutes.
Stir in the cream if using. Taste and season with salt and pepper. The sausage and broth add salt, so adjust carefully.
Serve: Ladle into bowls and top with Parmesan and fresh herbs.
A drizzle of good olive oil on top is a nice touch.