Combine first 4 ingredients in a large Dutch oven; bring to a boil. Reduce heat; cover and simmer 2 hours. Remove chicken from broth; let cool slightly. Remove meat from bones, discarding bones; chop meat into bite-size pieces. Strain broth, reserving 1 quart. Discard quartered onion and celery. Reserve remaining broth for use in other recipes.
Sauté mushrooms and chopped onion in butter in a large Dutch oven until tender. Stir in flour. Cook over medium heat 5 minutes, stirring constantly. Gradually add reserved 1 quart chicken broth; cook over medium heat, stirring constantly, until thickened and bubbly. Stir in reserved chicken, pimiento, salt, and pepper. Remove from heat, and keep warm.
Cut a slice from top of each Kaiser roll to form a lid; set aside. Remove soft center from each roll, and reserve for other uses, leaving shells intact. Place rolls and lids on baking sheets. Bake at 350° for 8 minutes or until lightly browned and crisp.
Spoon warm chicken mixture into rolls. Place each filled roll and lid on an individual serving plate, and serve immediately.