Spread out the puff pastry sheets and let them thaw for about 10 minutes at room temperature. Sort the blackberries, wash briefly and dab dry. Mix with coconut flakes and vanilla sugar.
Spread the edges of the puff pastry sheets with a little milk. Spread some blackberry filling on one half of each plate, leaving a 1 cm wide edge. Cut the other half of the pastry several times diagonally with a knife, but do not cut the edge.
Fold the cut-in half of the pastry over the filling and press it firmly together at the edges.
Place blackberry bags on a baking tray lined with baking paper. Spread with the remaining milk and sprinkle with sugar. Bake in a hot oven (electric cooker: 200°C/circulating air: 175°C/gas: level 3) for 15-20 minutes.
Dust the blackberry coconut bags with icing sugar and eat warm with vanilla ice cream.