Mix all dry ingredients together in a bowl. In a smaller bowl, mix water and melted fats together. Add wet ingredients to dry and mix until it forms a dough that is soft and elastic. Cover and let rise in a warm area until nearly double in size. Punch down and form dinner rolls, placing them in a greased 8x8-inch square metal baking pan. Allow to rise again until nearly double in size. Brush top of rolls gently with egg and milk mixture. Bake at 350°F for 15-20 minutes, or until golden and sounds hollow when tapped gently. Remove from pan and allow to cool on a rack. Yields 24 rolls.