4thick slices of artisan style country breadtoasted just before serving
Add the olive oil to a large deep skillet with a lid. Cook the onions and carrots over medium heat with ½ teaspoon salt until softened, about 8 minutes. Add the garlic, thyme, and paprika and cook for 1 minute. Stir in the cabbage, raise the heat to high and cook, stirring, until it starts to take on some color. Pour in the tomato sauce and stir, scraping up any brown bits that are stuck to the bottom. Add the beans.
If using a slow cooker, transfer the mixture to the slow cooker and pour in 2 cups of chicken stock or vegetable stock. Add another teaspoon of salt, freshly cracked black pepper, stir, and set to medium heat. Set the timer for 3 hours.
If completing the dish on the stovetop, pour in 3 cups of chicken stock or vegetable stock, add the remaining teaspoon of salt, and bring to a simmer. Cook over medium heat, partially covered, for 20 minutes. It should still be brothy, but reduced somewhat.
Just before serving, taste for seasoning and add more salt and black pepper if needed, and remove the thyme sprigs. Squeeze the lemon juice over and stir.
To serve, place the bread in the bottom of each of 4 bowls. Ladle the cabbage on top, then top with the shredded cheese.