In a covered large saucepan cook potatoes in enough boiling salted water to cover for 5 minutes. Add carrot and celery. Cook about 10 minutes more or until vegetables are tender; drain. Transfer 1 cup of the cooked vegetables to a small bowl; set the remaining cooked vegetables aside. Using a potato masher, mash the 1 cup vegetables until nearly smooth.
In the same saucepan melt butter over medium heat. Stir in flour, salt, and pepper. Gradually stir in the 1 1/2 cups milk. Cook and stir until slightly thickened and bubbly.
Stir in the reserved cooked vegetables, the mashed vegetables, and broth. Cook and stir over medium heat until heated through. If necessary, stir in enough additional milk to reach desired consistency. If desired, sprinkle each serving with cheese.