Heat the butter and oil in a small saucepan until the butter has melted.
Unfold the pastry on a lightly floured surface and separate into sheets. Brush lightly with the butter mixture, then cut into 24 pieces, each 10 x 8 cm (4 x 3½ inches).
Arrange a piece in each of the sections of a deep 12-hole muffin tin, then add a second piece at a slight angle to the first pieces to give a pretty jagged edge to each pastry case.
Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 6–8 minutes until golden. Meanwhile, warm the jam and orange juice in a saucepan, then add the nectarines and blueberries and warm through.
Lift the tart cases carefully out of the muffin tin and transfer to a serving dish. Fill the cases with the warm fruits and dust with sifted icing sugar. Serve with cream or ice cream (see below).