Combine eggs, milk, chicken broth, onion, paprika, and salt in a large mixing bowl; beat well. Stir in chicken, breadcrumbs, and rice. Pour mixture into a greased 8 1/2- x 4 1/2- x 3- inch loaf pan. Place in a shallow pan containing 1 inch hot water.
Bake at 350° for 50 minutes or until a knife inserted in center comes out clean. Cool 10 minutes in pan; unmold onto a warm serving platter. Serve with Almond-Mushroom Sauce. Garnish with parsley.