Place bread in a food processor; pulse 10 times or until coarse crumbs measure 1 cup. Place breadcrumbs in a medium bowl; set aside.
Place chicken in food processor, and pulse until ground. Add chicken, 1/2 teaspoon salt, nutmeg, pepper, and egg white to breadcrumbs in bowl; stir until combined. Shape mixture into 16 (1 1/2-inch) meatballs.
Heat oil in a large nonstick skillet over medium-high heat. Add meatballs; cook 6 minutes, browning on all sides. Remove meatballs from pan. Add the remaining 1/4 teaspoon salt, chicken broth, and flour to pan, stirring with a whisk until combined. Bring to a boil, and cook 1 minute or until slightly thickened, stirring constantly. Stir in sour cream, and return the meatballs to pan. Reduce heat to medium-low; cook for 10 minutes or until meatballs are done and sauce is thick. Sprinkle with parsley
Tip: Substitute white or whole wheat bread for the rye to bind the meatballs.