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 chopped onion and cook for 5 minutes until softened.
Add the minced garlic to the skillet and cook for 1 more minute until fragrant. Remove from heat.
In a large mixing bowl, combine the cooked cabbage, sautéed onion and garlic, shredded cheddar cheese, shredded mozzarella cheese, sour cream, mayonnaise, whole milk, salt, black pepper, and smoked paprika. Mix well until all ingredients are evenly incorporated.
Transfer the cabbage mixture into a greased 9×13 inch (23×33 cm) baking dish and spread evenly.
In a small bowl, combine the crushed buttery cracker crumbs with the 2 tablespoons of melted butter. Mix until the crumbs are evenly coated.
Sprinkle the cracker topping evenly over the cabbage mixture in the baking dish.
Bake the casserole in the preheated oven for 40 to 45 minutes, until the topping is golden brown and the casserole is bubbly.
Remove from the oven and allow to cool for 5 minutes before serving.