Brown the sausage: Heat a large pot or Dutch oven over medium heat.
Add sausage and break it up with a spoon. Cook until browned and no longer pink, about 6–8 minutes. If there’s excess fat, spoon it off, leaving about 1 tablespoon.
If the sausage is lean, add a splash of olive oil.
Sauté the aromatics: Add the diced onion. Cook until softened and lightly golden, 4–5 minutes. Stir in garlic and cook 30 seconds, just until fragrant.
Build the base: Add carrots and celery if using.
Sprinkle in Italian seasoning and red pepper flakes. Stir to coat the sausage and veggies with the spices.
Add potatoes and broth: Stir in the diced potatoes and pour in the chicken broth. Scrape up any browned bits from the bottom of the pot—those add big flavor.
Simmer: Bring to a gentle boil, then reduce the heat to a simmer.
Cook uncovered for 12–15 minutes, or until the potatoes are fork-tender.
Add the greens: Stir in the kale or spinach. Simmer another 2–3 minutes, until the greens are wilted and tender.
Make it creamy: Lower the heat. Stir in the cream and Parmesan.
Do not let it boil hard after adding dairy. Taste and season with salt and pepper as needed.
Serve: Ladle into bowls and top with extra Parmesan and a sprinkle of chopped parsley if you like. Serve with crusty bread.