Preheat the oven to 350 degrees F (175 degrees C).

Dissolve bouillon cubes in water in a large pot over medium-high heat. Add cabbage and carrots; cook until tender, 20 to 30 minutes. Drain; reserve 1/2 cup cooking liquid. Transfer cabbage and carrots to an 8x11-inch casserole dish.

Melt butter in a saucepan over medium heat; stir in flour until hot, about 1 minute. Stir in reserved cooking liquid and milk until smooth. Add Cheddar cheese; cook and stir until cheese is melted and mixture is smooth and thick. Pour cheese sauce over cabbage and carrots; stir to coat. Season with paprika.

Bake in the preheated oven until hot and bubbly, 20 to 30 minutes.