Melt butter in a small skillet. Stir in flour to make a paste. Gradually add chicken broth and milk. While stirring, cook until mixture thickens. Stir in Cheddar cheese and 2 tablespoons Parmesan cheese salt and pepper. Stir until cheese melts.
Place cooked asparagus in an oven proof baking plate. Pour cheese sauce over asparagus. Sprinkle with remaining 1 tablespoon Parmesan. Place under broiler, and broil until surface is lightly browned.