Heat 1 tablespoon of the oil in a large, heavy-bottomed pot over medium heat. Brown the sausage slices, flipping often, until they’re golden on all sides. Remove the slices from the pot and set them aside.
Heat the remaining tablespoon oil in the same pot over medium heat. Add the onion, celery, and carrots. Cook the vegetables, stirring occasionally, for 6-8 minutes, or until the onion is translucent and all of the vegetables are tender. Add the garlic to the pot. Continue to cook the vegetable and garlic mixture for 1-2 minutes, stirring often, or until the garlic is very fragrant.
Add the tomatoes, potatoes, Italian seasoning, and broth to the pot. Raise the heat and bring this mixture to a boil. Reduce the heat to low, cover, and simmer for 12-15 minutes, or until the potatoes are tender. Stir in the kale. Simmer for another 5-8 minutes, or until the kale is tender. Stir in the cooked sausage, vinegar, and vegan parmesan. Continue to simmer until all of the ingredients are heated through. Transfer the soup to bowls and serve.
Notes
The soup can be stored in an airtight container in the fridge for up to 1 week and frozen for up to 1 month.