In a bowl, combine 3 cups cooled, cooked rice, 3 slightly beaten eggs, 1/3 cup flour, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Cut 3 ounces American cheese into 1/2 inch cubes. For each rice ball with wet hands, shape about 2 tablespoons of the rice balls in 1/2 cup finely crushed cracker crumbs. In a skillet, heat 1/2 inch cooking oil. Fry rice balls 4 or 5 at a time until golden brown. Drain on paper towels. Keep warm.

Vegetable Sauce: In a small saucepan, cook 2 tablespoons chopped green pepper, 2 tablespoons chopped onion, and 2 tablespoons butter until tender but not brown. Add 2 tablespoons flour, 1/2 teaspoon salt, and dash of pepper. Add 1 1/4 cups milk, all at once. Cook and stir until thickened. Cook 1 minute more. Add any remaining cheese cubes, stirring until melted. Pour vegetable sauce over rice balls.