2 ounces shredded Cheddar cheese, or more to taste
1/4 teaspoon paprika, or to taste
Preheat oven to 350 degrees F (175 degrees C).
Dissolve bouillon cubes in water in a large pot over medium-high heat. Cook cabbage and carrots in the seasoned water until tender, 20 to 30 minutes. Drain, reserving 1/2 cup of the cooking liquid. Transfer cabbage and carrots to an 8x11-inch casserole dish.
Melt butter in a saucepan over medium heat. Stir flour into melted butter until hot, about 1 minutes. Pour reserved cooking liquid and milk into the flour mixture; stir until smooth. Add cheese to milk mixture; cook and stir until cheese is melted and the mixture is smooth and thick. Pour cheese sauce over cabbage and carrots; stir to coat. Season with paprika.
Bake in preheated oven until hot and bubbly, 20 to 30 minutes.