Cut the puff pastry into 9 (3-inch) rings using a ring mold or a sharp paring knife.
Place the rounds on a parchment-lined baking sheet and bake in the oven for 10 to 15 minutes, or until golden brown.
Combine the black cherries, pineapple juice, and maraschino cherry juice in a small sauce pan. Bring to a simmer over medium heat.
Transfer the mixture to a blender or food processor and puree until smooth. Pass the sauce through a mesh sieve. Set aside to cool.
To make the pineapple: Dust the pineapple with confectioners' sugar and place in a baking dish. Cook in oven for 15 minutes, or until golden at the edges.
Let cool.
To make the Chantilly cream: Using a whisk, or hand blender, blend the heavy cream, sugar, and vanilla until fluffy and stiff peaks form. Keep the mixture chilled until ready to use.
To make the custard: In a small sauce pan over medium heat, simmer the pineapple juice until its reduced by half. Set aside and let cool. In a separate small sauce pan over low heat, simmer the milk with the vanilla bean until warm. Using a whisk, beat the egg yolks with the sugar, add the flour and stir in the warm milk.
Pour the mixture into a pot and cook over medium heat, stirring occasionally, until the cream is smooth, but not too thick. Stir in the pineapple reduction.
Transfer the custard to a bowl, cover the surface with plastic wrap and allow to cool. When the custard is cool, transfer to a large pastry bag fitted with a wide round pastry tip.
Place a puff pastry disk on the plate. Pipe the custard over the pastry in circles and place a slice of caramelized pineapple on the custard. Cover with another disk of puff pastry and pipe some Chantilly cream on top. Top with one more pastry round and drizzle with cherry maraschino sauce.
