In a large saucepan, combine orange juice, cinnamon and vanilla extract over medium-high heat. Bring mixture to a boil, and reduce to low heat. Simmer 10 minutes.
Remove cinnamon sticks. Stir in ice cream.
Cook over low heat, stirring constantly, until heated through. Do not allow mixture to boil.
Serve with additional scoops of ice cream or miniature marshmallows, if desired.