Melt 1 tablespoon unsalted butter in a heavy‑bottomed pot (such as a Dutch oven) over medium heat. Add 1 pound bulk mild Italian sausage meat (broken up into bite‑sized pieces) and brown, stirring and breaking up the meat, until browned on all sides (about 3 minutes). If the pot is overcrowded, brown the meat in batches. Using a slotted spoon, transfer the browned sausage to a paper‑towel‑lined plate and set aside.
Spoon out and discard all but 1 teaspoon of the fat in the pot. Add 1 small onion (4 to 5 ounces), finely diced, and 2 celery ribs, diced. Sauté until the onion and celery are starting to soften, about 3 minutes. Add 2 garlic cloves, minced or pressed, and ½ teaspoon smoked hot paprika; cook, stirring, until fragrant, about 30 seconds.
Add 3 cups chicken broth and 1 cup water to the pot. Cover and bring to a simmer. Add 2 cups small broccoli florets and the reserved browned sausage. Cover and simmer until the broccoli is tender and the sausage is fully cooked, about 5 minutes.
Remove the lid and stir in 1 teaspoon dried oregano (or 1 tablespoon chopped fresh oregano), ½ cup heavy cream, and ¼ cup grated Parmesan cheese. Stir in 1 to 2 splashes liquid smoke to taste. Continue cooking, stirring, until the soup is heated through and the cheese has melted (about 1–2 minutes).
Equipment
Measuring spoons and cups
Knife and cutting board
garlic press (optional)
heavy-bottomed pot, such as a Dutch oven
Wooden Spoon
Slotted spoon
Paper Towels
Spoon
Notes
Recipe notes:
* Liquid smoke is a powerful ingredient. I suggest you start with 1 splash, then taste the soup and add more to taste.