In a mixing bowl, using your fingertips, combine the dry ingredients with the butter, until it resembles coarse bread crumbs. It takes a few minutes but it will eventually come together.
Add the egg yolk mixture and combine until you get large clumps. Turn the pastry out onto a work surface and form it into a disc. Wrap the pastry in cling wrap and refrigerate for at least 20 minutes.
Make sure to take the pastry out and let stand at room temperature for 10 minutes before rolling.
On a lightly floured work surface, roll out two-thirds of the pastry to an 11 1/2-inch round. Gently lift the pastry with a tray or the rolling pin and transfer it to a 9-inch tart pan 1 inch deep. Press into the pan, folding in the overhanging dough to reinforce the sides. Trim the overhang and knead the scraps into the remaining dough.
Dust the work surface with flour again and roll out the remaining pastry to a 9 1/2-inch round. Using a pastry wheel, cut the round into 3/4-inch-wide strips.
Preheat the oven to 180°C. In a bowl, toss the blackberries, apples, sugar and flour; spoon into the tart shell. Scatter the butter on top. Arrange the strips over the berries in a lattice pattern, pressing the ends onto the pastry rim. (Just think over under and start from one corner of the pie) Trim any excess pastry. Brush the lattice with the egg yolk mixture and sprinkle with a little extra sugar.
Bake the tart for about 45 minutes to an hour, or until the pastry is golden and the juices are bubbling. Transfer to a wire rack and allow to cool.