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Whirl the flour, salt and sugar in food processor, fitted with the steel blade. Add the chopped nuts and process to combine. Add the egg to ¼ cup water in a cup with a spout and stir with a fork to break up the egg. Add 1 teaspoon vanilla and stir. Pulse the cold butter into the dry ingredients until the butter cubes are no larger than the size of small peas. Add enough of the egg/ice water mixture in increments until the dough is moist, but not overly wet and it holds together when pinched between two fingers.
Turn the mixture out of the machine and, using the heal of your working hand, schmear the dough outward—in 1 inch increments, on your work surface (going away from you). Gather the dough using a pastry scraper and do this again. Gather dough, enclose in plastic wrap, flatten into a disk and chill well.
Roll dough between sheets of floured wax paper. When the dough is 1/4 inch thick, remove the top sheet of paper and brush any excess flour off from both sides of the dough. Using a 2 ½ to 3-inch cookie cutter (fluted) –cut out circles of dough. Dip the cutter into powdered sugar to keep it from sticking. For larger pastries, use a. 4 to 6 inch cutter). Line a large baking sheet with wax paper. Place the cut circles of dough onto the sheet (layer between sheets of wax paper Cover with plastic and chill until the dough firms up, 10 to 30 minutes.
Place a spoonful of fruit filling in the center of each pastry round. Pull up the edges and pinch, creating triangles. Cover the sheet with plastic wrap and chill 1 hour (or overnight). Fill each circle, square off and pinch edges. Place on tray, cover and chill.
Preheat the oven to 375F. Line cushioned cookie sheets with parchment. Make the egg wash by mixing the egg with the water and vanilla. Strain this into another bowl. Brush chilled pastries with egg wash (surrounding the fruit filling) and sprinkle the top pastry generously with the nut allowing the filling to be exposed. Bake for 15 minutes (or until golden). Bake 20 minutes for larger pastries. Cool on wire racks.