Preheat the oven to 350°F (175°C).
Bring a large pot of salted water to a boil. Add the chopped cabbage and cook for 5 minutes until slightly tender. Drain well and set aside.
In a large skillet, melt 2 tablespoons of butter over medium heat. Add the diced onion and cook for 5 minutes until softened.
Add the minced garlic to the skillet and cook for 1 minute until fragrant.
Sprinkle the flour over the onions and garlic, stirring constantly for 2 minutes to form a roux.
Gradually whisk in the milk, stirring constantly to avoid lumps. Cook for 3-4 minutes until the sauce thickens.
Remove the skillet from heat and stir in the sour cream, salt, black pepper, smoked paprika, shredded cheddar cheese, and shredded mozzarella cheese until the cheese melts and the sauce is smooth.
Add the drained cabbage to the cheese sauce and stir until well combined.
Transfer the cheesy cabbage mixture to a greased 9×13 inch casserole dish and spread evenly.
In a small bowl, combine the crushed crackers with the melted butter. Sprinkle the cracker topping evenly over the casserole.
Bake in the preheated oven for 30-35 minutes until the topping is golden brown and the casserole is bubbly.
Remove from the oven and let cool for 5 minutes before serving.