In a medium bowl, beat cream until it begins to thicken. Add sugar and vanilla; beat until stiff peaks form. Refrigerate until serving.
In a 6-qt. stockpot, heat milk, cream, cinnamon sticks, pie spice and orange zest over medium heat until bubbles form around sides of pan.
Whisk pumpkin, sugar and baking chips into milk mixture until blended. Remove from heat; stir in vanilla. Discard cinnamon sticks. Pour into mugs; top with whipped cream. Sprinkle with additional pumpkin pie spice. Serve immediately.