Bring a large pot of salted water to a boil and carefully place the whole head of cabbage into the water. Boil for 10-12 minutes until the outer leaves become tender and pliable, then remove with tongs and let cool slightly. Once cool enough to handle, carefully peel away the softened leaves and set aside on a clean kitchen towel. While the cabbage cooks, combine the ground beef, cooked rice, eggs, minced onion, diced green pepper, grated carrots, parsley, smoked paprika, salt, and pepper in a large bowl. Mix gently with your hands until just combined—don't overmix, as this keeps the rolls tender. I like to add a pinch extra salt to the filling since the sauerkraut will provide tang; this balance creates a more complex flavor.
Pat the reserved cabbage leaves dry and lay them flat on your work surface. Using a small knife, carefully trim out the thickest part of the center vein from each leaf to make rolling easier without tearing the delicate leaves. Place about 1/3 to 1/2 cup of the meat filling from Step 1 toward the bottom of each leaf, fold in the sides, then roll tightly away from you to create a compact cylinder. Arrange the rolled cabbage rolls seam-side down on a clean plate. I recommend making sure your rolls are snug but not overstuffed—this prevents them from unraveling during the long cooking time.
In a large bowl, whisk together the tomato sauce, tomato soup, and diced tomatoes until well combined. This creates a balanced sauce that's neither too acidic nor too thick. Taste and adjust seasoning if desired—remember that the sauerkraut will add significant flavor and saltiness, so season conservatively at this stage.
Rinse and drain the sauerkraut well to control its tanginess and remove excess liquid. Choose your cooking vessel based on your preferred method: a Dutch oven for stovetop, a slow cooker for hands-off cooking, or a 9x13 inch baking dish for the oven. Spoon a thin layer of the sauce mixture from Step 3 onto the bottom of your chosen vessel to prevent sticking. Arrange half of the cabbage rolls from Step 2 seam-side down in a single layer, then scatter half of the drained sauerkraut over them. Pour about one-third of the remaining sauce over this layer, then arrange the remaining cabbage rolls, followed by the remaining sauerkraut, and finally the remaining sauce. Nestle the 2 bay leaves into the mixture for subtle flavor throughout.
For stovetop: Cover the pot, bring to a simmer over medium heat, then reduce to low and cook for 3-4 hours, stirring gently every hour. For slow cooker: Cover and cook on high for 4-6 hours or on low for 6-8 hours. For oven: Cover the baking dish tightly with foil and bake at 350°F for 1 hour, checking that the meat reaches 165°F on an instant-read thermometer. The long, gentle cooking allows the flavors to meld together and the meat to become incredibly tender. Regardless of method, the rolls are done when the meat is fully cooked, the cabbage is very tender, and the sauce has thickened slightly. Remove the bay leaves before serving.