Combine first 6 ingredients and water to cover in a Dutch oven; bring to a boil. Cover; reduce heat, and simmer 1 hour or until chicken is tender. Remove chicken from broth; cool. Strain broth, reserving 2/3 cup. Discard vegetables. Bone chicken, and chop meat. Place chopped chicken in a 12- x 8- x 2-inch baking dish.
Combine breadcrumbs, onion, chopped parsley, savory, and pepper in a small mixing bowl. Stir in reserved broth; mix well. Set aside 3 tablespoons stuffing mixture. Spoon remaining stuffing in center of each slice of ham, and roll up tightly. Arrange ham rolls, seam side down, around chicken in baking dish.
Melt butter in a heavy saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add half-and-half; cook over medium heat, stirring constantly, until thickened and bubbly. Stir in nutmeg. Spoon sauce over chicken and ham rolls; sprinkle with reserved stuffing. Bake, covered, at 350° for 15 minutes. Uncover, and bake an additional 15 minutes.