Start by chopping the sausage into bite-sized pieces. Sear them in a skillet over medium heat until deeply golden and slightly crispy, about 5-7 minutes. This step enhances the smoky flavor and adds richness to the soup.
While the sausage cooks, dice the carrots into small cubes or slices, and finely chop the onion. These vegetables will soften and release their sweet aroma during cooking.
Transfer the cooked sausage to the slow cooker. Add the diced carrots, chopped onion, undrained diced tomatoes, and broth. Stir everything together to combine evenly.
Peel and dice the potatoes into roughly 1/2-inch pieces, then add them to the slow cooker. Sprinkle in smoked paprika for a smoky depth, and season with salt and pepper to taste.
Cover the slow cooker and set it to low. Let it simmer gently for 6-8 hours until the vegetables are tender, the sausage is cooked through, and the flavors meld into a fragrant, hearty broth.
During the last hour, taste the soup and adjust the seasoning with additional salt, pepper, or smoked paprika if needed. The soup should be thick, with a vibrant orange hue from the carrots and a smoky aroma filling the air.
Once ready, turn off the slow cooker and let the soup sit for 5 minutes. Stir gently to distribute the flavors, then serve hot in bowls, garnished with fresh herbs if desired. Enjoy the comforting warmth and rustic texture of this slow-cooked sausage soup.
