Brown the sausage: Heat a large pot or Dutch oven over medium heat. Add the sausage and cook, breaking it into small pieces, until browned and cooked through, about 6–8 minutes.
If there’s a lot of fat, spoon off excess, leaving about 1–2 tablespoons for flavor.
Sauté the aromatics: If the pot looks dry, add olive oil. Stir in the onion, celery, and carrots. Cook until softened, about 5–7 minutes, scraping up browned bits.
Add the garlic and cook 30 seconds until fragrant.
Season the base: Sprinkle in oregano, thyme, and red pepper flakes. Add the bay leaf. Stir to coat the vegetables and sausage with the spices.
Add broth and potatoes: Pour in the chicken broth and bring to a boil.
Stir in the potatoes and reduce heat to a gentle simmer.
Simmer until tender: Cook uncovered for 12–15 minutes, or until the potatoes are easily pierced with a fork. Taste and season with salt and pepper as needed.
Make it creamy: Lower the heat. Stir in the heavy cream and let the soup warm through without boiling, about 2–3 minutes.
This keeps the texture silky.
Add greens: Fold in the kale or spinach and cook until wilted, 2–3 minutes. Remove the bay leaf. Adjust seasoning again—salt, pepper, and a pinch more red pepper if you like heat.
Finish and serve: Ladle into bowls.
Top with chopped parsley and Parmesan if using. A squeeze of lemon brightens the richness—add a little at the table to taste.