Preheat your oven to 400°F.
In a high-sided, ovenproof skillet, heat 2 tablespoons of olive oil over medium-high heat. Add the ground beef, chopped onion, and 1/2 teaspoon salt. Cook, breaking up the meat with a spoon, until browned and cooked through (about 6–7 minutes).
Add chopped garlic and crushed red pepper, stirring constantly until fragrant (1 minute).
Stir in the cabbage and cook, stirring frequently, until mostly tender (about 5–8 minutes).
Add the diced tomatoes, tomato sauce, microwaveable brown rice, balsamic vinegar, caraway seeds, paprika, 1 tablespoon of parsley, and the remaining 3/4 teaspoon salt. Mix thoroughly and spread into an even layer.
Remove the skillet from the heat and sprinkle mozzarella evenly over the top.
Bake in the preheated oven until the cheese is melted and lightly browned (approximately 15 minutes).
Garnish with the remaining parsley before serving.