Place bread cubes on a jelly-roll pan, and bake at 375° for 15 minutes or until toasted.
While the croutons bake, combine onion, carrot, and celery in a food processor, and pulse until chopped. Melt butter in a large saucepan over medium-high heat. Add vegetables; sauté 5 minutes or until tender.
Lightly spoon flour into dry measuring cups; level with a knife. Gradually add 1 can of broth to flour in a medium bowl; stir well with a whisk. Add flour mixture to pan. Stir in 1 can of broth; bring to a boil. Reduce heat to medium, and cook 10 minutes or until thick. Stir in milk, salt, paprika, and pepper; cook for 10 minutes. Remove from heat; add the cheese, and stir until cheese melts. Ladle soup into bowls, and top with croutons.