Start by chopping your sausage into bite-sized chunks, then set aside. Dice the onion, carrots, and celery into small, even pieces to ensure they cook evenly and look appealing in the final dish.
Heat your slow cooker on high and add a tablespoon of oil if needed. Sear the sausage chunks in a skillet over medium-high heat until they develop a golden, crispy crust—this will take about 5 minutes and fill your kitchen with a savory aroma. Transfer the browned sausage to the slow cooker.
In the same skillet, sauté the diced onion, carrots, and celery for about 3-4 minutes until fragrant and slightly softened. This step enhances their sweetness and flavor. Add the sautéed vegetables to the slow cooker.
Pour in the broth along with the can of diced tomatoes and their juice. Stir everything together, making sure to scrape up any browned bits from the skillet for extra flavor. Season with salt, pepper, and a dash of smoked paprika if you like a smoky taste.
Cover the slow cooker and set it to low. Let it cook for 6-8 hours, or on high for 3-4 hours. The kitchen will fill with a rich, savory smell, and the vegetables will become tender while the sausage stays juicy.
About 30 minutes before serving, stir in chopped greens like spinach or kale if desired. Cover and let the greens wilt into the broth, adding a burst of freshness and color.
Once the greens are wilted and the flavors are melded, give the soup a final taste and adjust the seasoning with more salt and pepper if needed. Ladle the hot, fragrant soup into bowls and enjoy the comforting, hearty flavors with crusty bread or your favorite side.