Stir together milk and pumpkin in a saucepan; cook over low heat until steaming. Stir in vanilla and cinnamon. With a handheld blender or electric mixer, blend for 15 to 20 seconds, or until thick and foamy. Pour into 4 to 6 mugs or tall glasses; pour in hot coffee. If desired, top with whipped cream, sprinkle with spice and add cinnamon stick stirrers. Serve immediately.