Heat a large, deep skillet or Dutch oven over medium-high heat and add the ground beef and pork, breaking it apart with a spoon. Cook until the meat is browned and no longer pink, about 6-7 minutes. Drain and set aside.
In the same skillet, heat 1 tablespoon of olive oil over medium high heat. Add the onion and cook until it is tender and translucent, about 7-8 minutes. Add the garlic and cook until it is fragrant, about 30 seconds.
Pour in the diced tomatoes and tomato juice. Add the beef, pork, 1 teaspoon salt, dill, thyme, paprika, and black pepper and bring to a simmer. Reduce the heat to low, cover and cook until the sauce has slightly thickened, about 15 minutes. Stir in the cooked rice and set aside.
Meanwhile, heat the remaining tablespoon of olive oil in a separate large skillet over medium high heat. Add the cabbage and 1 teaspoon of salt. Cook the cabbage, tossing often, until it is wilted and just tender, about 8-10 minutes.
Grease a 9x13 casserole dish with cooking spray. Layer half the cabbage on the bottom of the dish followed by the rice mixture, followed by 1 cup of the cheese. Repeat with the remaining ingredients.
Cover the dish tightly with aluminum foil, then transfer to the oven and bake for 30 minutes. Remove the foil and continue to bake until the cheese is bubbly and browned, about another 15 minutes. Garnish with fresh parsley before serving.