Prepare the Fillo Pastry:
Remove the fillo pastry from the refrigerator and allow it to come to room temperature while still in its packaging.
Preheat the Oven:
Preheat the oven to 180°C (350°F) fan-forced. Line a baking tray with parchment paper.
Prepare the Apricots:
Place the apricot quarters in a bowl and sprinkle with caster sugar. Toss gently and set aside.
Make the Cheesecake Filling:
In a mixing bowl, stir the softened cream cheese until smooth. Add the icing sugar, vanilla bean paste, and egg yolk. Mix until creamy and fully combined. Refrigerate until ready to use.
Assemble the Pastry Base:
Place one sheet of fillo pastry on a clean work surface and brush lightly with melted butter. Continue layering the remaining sheets, brushing each with butter and slightly rotating each sheet to create a large circular shape.
Add the Filling:
Spread the cheesecake mixture in the center of the pastry, leaving a border around the edges. Spread it into a circle approximately 20 cm (8 inches) wide.
Top with Apricots:
Arrange the sugared apricot quarters evenly over the cheesecake filling.
Form the Galette:
Fold the pastry edges inward over the outer edge of the filling, creating a rustic border.
Finish the Pastry:
Lightly whisk the egg white and brush it over the exposed pastry edges. Sprinkle generously with flaked almonds.
Bake:
Carefully transfer the galette to the prepared baking tray. Bake for 35 minutes, or until the pastry is golden brown and crisp.
Cool and Serve:
Remove from the oven and allow the galette to rest for 30 minutes before serving. Dust with icing sugar just before serving.