Preheat an oven to 180 degrees C. Place pie pastry onto a baking tray.
Toss the quartered apricots with the white sugar in a bowl.
Mix almond meal, icing sugar and egg together in another bowl to create a paste. Spread almond paste on the centre of the pastry leaving 1cm of bare crust all around the edge.
Arrange the sugared apricots over the almond paste. Fold the 1cm bare edge of the pastry inward over the almond paste and apricots leaving the centre of the tart uncovered. Crimp the edge down with a fork as you go around the tart.
Bake in the preheated oven until the crust is golden brown; about 40 minutes.
Brush the melted apricot jam over the hot galette. Slice and serve.