Set aside 4 of the pineapple rings. Add the remaining pineapple rings to a food processor, along with the ginger, salt and agave. Process until smooth and well combined.
Cut each sheet of puff pastry into 4 equal squares. Lay each square on a parchment-lined baking sheet, and spread 1 heaping tablespoon of the pineapple mixture on the center of each.
Brush the edges of the puff pastry with egg wash. Top each square with a second square of pastry and gently press the sides together to seal. Brush the top with egg wash, then top with a pineapple slice and sprinkle with sugar.
Bake until the sugar has caramelized, 20 to 22 minutes.
Serve with ice cream, drizzled with caramel and sprinkled with toasted almonds.