In a small saucepan over medium heat, combine the apple cubes with 200 ml apple juice, a squeeze of lemon juice, some grated lemon zest, a pinch of vanilla sugar, and some sugar.
Bring to a simmer and cook for 5 minutes, stirring frequently.
In a small bowl, mix some pudding powder with the remaining 100 ml apple juice until smooth.
After the 5 minutes are up, add the pudding mixture to the simmering apples and stir vigorously with a whisk. Bring to a boil over medium-high heat for 1 minute, then remove from heat.
Stir occasionally as the mixture cools to lukewarm, about 10 minutes.
Preheat the oven to 220 °C (425 °F) on top and bottom heat.
Remove the puff pastry sheets from the freezer and cut into squares using a pizza cutter or sharp knife. Lay on a work surface to thaw for about 5 minutes.
Stir some mascarpone into the cooled apple mixture.
Place roughly 1/2 to 1 tablespoon of the apple-mascarpone filling slightly diagonally in the center of a pastry square.
Fold the pastry diagonally in half to form a triangle.
Press the edges together firmly to seal, preventing any filling from leaking.
Transfer to a baking sheet and repeat with the remaining pastry squares and filling.
In a small bowl, whisk together 1 egg with a splash of milk.
Brush the egg-milk mixture over each pastry triangle and poke holes across the top with a fork.
Bake for 15 to 20 minutes until golden brown.
Serve warm from the oven, or let cool completely, refrigerate for 1 to 2 hours, and serve chilled.