Preheat oven to 400 Deg F. Set out a large baking sheet and place a piece of parchment paper on it. You may have to use two baking sheets.
Combine the cream cheese, jam and brown sugar and mix until smooth
Drain the canned pineapple rings and reserve the juice
Pit cherries if using fresh
Working with one sheet of puff pastry at a time, roll between pieces of wax paper to make it more square. Cut the pastry into 4 squares. Slightly fold over the edges of each square. Pierce the middle with a fork, being careful not to puncture all the way through the pastry. If the pastry is getting too warm set in the refrigerator to chill for a few minutes.
Working quickly, spread about 2 tablespoons of the cream cheese and jam mixture in the middle of each pastry square. Place a pineapple ring on top then place a cherry in the middle of the pineapple. Place on the prepared baking sheets about an inch apart. Repeat with the other square of puff pastry for a total of 8 pastries.
Whisk the egg and water together and brush the edges of the pastry. Sprinkle coarse sugar around the edges. If you have small baking sheets, bake 4 pastries at a time, keeping the other 4 chilled until ready to bake.
Bake 22-25 minutes or until the pastry is puffed and golden.
While the pastries are baking make the pineapple rum sauce.
Combine all of the sauce ingredients in a small saucepan and bring to a boil, stirring until the sugar is dissolved and the butter is melted. Lower to a strong simmer and let reduce while the pastries are baking.
Once the pastries are done, remove the sauce from the heat. Let both the pastries and sauce cool a few minutes before serving. Drizzle some of the sauce over the pastry before serving. If making for dessert add a scoop of vanilla or coconut ice cream!