Gather your slow cooker, a wooden spoon, a sharp knife, and a cutting board to prepare for cooking.
Slice the pork sausage into thick coins and chop the onions, carrots, and celery into bite-sized pieces, keeping everything within easy reach.
Set your slow cooker to low heat. If your sausage isn’t very fatty, add a splash of oil to help it brown. Add the sausage coins and cook for about 5 minutes, stirring occasionally until they start to turn golden and smell savory.
Add the chopped onions, carrots, and celery into the cooker with the sausage. Stir well and cook for another 5 minutes, watching as the vegetables begin to soften and release their sweet aroma.
Pour in the broth, then add the can of diced tomatoes along with their juice. Use your spoon to scrape the bottom of the cooker, lifting any browned bits that add deep flavor.
Season the mixture with thyme, a bay leaf, and salt and pepper to taste. Cover with the lid and cook on low for 6 to 8 hours, allowing the flavors to meld and the sausage to become tender.
After cooking, check that the sausage is cooked through and vegetables are tender—no pink in the sausage and vegetables easily pierced with a fork. Remove the bay leaf and give the soup a final stir.
Squeeze a little lemon juice or sprinkle fresh herbs on top if desired, then ladle the steaming, hearty soup into bowls to enjoy immediately.