Heat a large pot or Dutch Oven over medium heat. Crumble the sausage into the pot and cook until the sausage is brown and crispy, stirring occasionally and breaking up the sausage with a wooden spoon.
Meanwhile, dice the onions and chop the celery into chunky slices.
Remove the sausage from the pot and drain the excess fat if needed.
Add the butter to the pot, and add the onions, celery, and salt. Cook for 5 minutes, stirring occasionally.
Peel the carrots and slice them into coins. Add them to the pot with the onions and celery.
Mince the garlic, chop the tomatoes, and them to the pot.
Chop the potatoes into large chunks and add them to the pot along with the browned sausage.
Remove the thyme leaves from the stems, chop finely, and add to the pot.
Pour in the stock. There should be enough liquid to barely cover the soup ingredients. Bring the soup to a boil, reduce the heat, and simmer until the potatoes are tender—around 10-15 minutes.
Once the potatoes are tender, turn off the heat and add the cream, the pepper, and the parsley.
Taste for seasoning and enjoy!