In a large pot, bring potatoes, celery and onion to a boil in 2 cups of broth. Cook until potatoes are tender, 15 minutes. Drain and reserve liquid.
Combine reserved broth and half-and-half in pot. In a bowl, combine melted butter and flour. Stir into half-and-half mixture over medium heat. Stir until thickened. Stir in reserved vegetables, remaining broth, bouillon and pepper. Heat through and serve.