Chop the onion into small dice, slice the carrots into thick rounds, and cube the potatoes. Set all aside for easy access.
Heat a skillet over medium heat and add the sausage, breaking it apart with a spatula as it browns. Cook until evenly browned and fragrant, about 5-7 minutes.
Transfer the cooked sausage to the slow cooker. In the same skillet, sauté the diced onion and smashed garlic until the onion turns translucent and fragrant, about 3-4 minutes.
Add the sautéed onions and garlic to the slow cooker, then pour in the vegetable broth along with the sliced carrots, cubed potatoes, and canned tomatoes with their juices. Stir everything together.
Cover the slow cooker with the lid and set it to low. Let it cook for 6-8 hours, allowing the sausage to break down into the broth and the vegetables to become tender.
Check the soup after about 6 hours. The sausage should be crumbled and integrated into the broth, and the vegetables tender. Adjust seasoning with salt and pepper as needed.
Ladle the hot sausage soup into bowls. Garnish with fresh herbs if desired, and serve steaming, hearty, and comforting.
