Remove shells from eggs, and halve lengthwise, remove and mash the egg yolks. Combine mashed yolks with the mayonaise or salad dressing, prepared mustar, the 1/8 teaspooon salt, and dash of pepper. Refill egg whites with the yolk mixture; set aside.
In a saucepan bring chicken broth to boiling. Add uncooked rice and celery; return to boiling. Reduce heat; cook, covered, for 15 minutes. Mean, while, prepare cheese sauce. In medium pan melt butter; stir in flour, the 1/2 teaspoon salt, and dash of pepper. Add milk all at once; cook and stir till thickened and bubbly. Cook and stir 1 to 2 minutes more. Stir in cheese and heat till melted; set aside.
Stir ham and 1 cup of the cheese sauce into the rice. Turn into a 12x 7 1/2x2-inch baking dish. Arrange the deviled eggs atop rice mixture, pressing each lightly into rice mixture. Sprinkle with paprika. Bake, covered, in a 350 oven for 25 to 30 minutes or till heated through.