Preheat the oven to 400°F (200°C).
Roll out the puff pastry slightly and place it on a lined baking tray.
Score a 1-inch border around the edges without cutting through and prick the center with a fork.
Bake the pastry for 15-18 minutes until golden and puffed, then let it cool completely.
In a bowl, combine the cream cheese or mascarpone, powdered sugar, and vanilla extract until smooth.
Spread a thin layer of the cream mixture inside the baked pastry center.
Heat the heavy cream in a saucepan until just simmering; do not boil.
Pour the hot cream over the chopped dark chocolate and let sit for 2 minutes.
Stir the mixture until smooth and glossy to create the ganache.
Pour the ganache evenly over the cream layer in the tart.
Refrigerate the tart for 1 hour until the ganache is set but still soft.
Decorate the tart with chocolate curls or shavings, slice, and serve.