Preheat oven to 375°F. Grease a 9x13-inch baking dish.
Warm olive oil in a large skillet over medium heat. Soften onion for 4 to 5 minutes.
Stir in garlic and cook until fragrant, about 30 seconds.
Add cabbage. Cook, tossing often, until wilted and slightly tender, 8 to 10 minutes.
Pour in broth. Cover to steam 3 minutes, then uncover and reduce most of the liquid.
Season with salt, black pepper, paprika, thyme, and red pepper flakes. Remove from heat.
Whisk sour cream, cream cheese, and mayonnaise in a large bowl until smooth and creamy.
Fold in half the cheddar and half the mozzarella.
Combine the warm cabbage mixture with the creamy cheese mixture. Adjust seasoning to taste.
Spread into the baking dish. Top with remaining cheddar and mozzarella.
Mix breadcrumbs, Parmesan, and melted butter. Sprinkle evenly over the casserole.
Bake until bubbly and golden, 22 to 25 minutes. Rest 10 minutes, garnish with parsley, and serve.
Notes
Variation: Add 1 cup cooked crumbled bacon or sautéed mushrooms to the cabbage for extra savoriness. Storage: Refrigerate leftovers in an airtight container for up to 4 days; reheat covered at 350°F until warm.This recipe is an original creation inspired by classic Cheesy Cabbage Casserole Recipe flavors. All ingredient ratios and instructions are independently developed.