Combine pineapple, apple, sugar, orange rind, juice and cinnamon sticks in 5-quart saucepan. Bring to a boil over medium-high heat. Reduce to medium-low; simmer, uncovered, stirring occasionally, until pineapple is translucent and most of liquid is absorbed, about 1 hour 10 minutes.
Remove saucepan from heat. Carefully press with potato masher until desired consistency (do not crush cinnamon sticks). Cook another 15 minutes or until desired thickness.
Remove from heat. Stir in vanilla. Let cool completely.
When cooled, remove and discard sticks and rind. Pack in gift jars. Keep refrigerated for up to 3 weeks.