Preheat oven to 350 degrees. On a lightly floured work surface, roll out puff pastry to a 12-by-16-inch rectangle.
Transfer to a parchment-lined rimmed baking sheet and trim to make a neat rectangle. Freeze until firm, 10 minutes. With a fork, prick pastry all over. To prevent pastry from rising, top with a sheet of parchment paper and stack another rimmed baking sheet on top.
Bake until light golden, 20 to 25 minutes.
Meanwhile, in a food processor, combine 1/4 cup pistachios and sugar and process until pistachios are finely ground.
Sprinkle mixture on pastry, leaving a 3/4-inch border.
Bake until pastry is deep golden and pistachio mixture begins to turn golden, 15 to 17 minutes. Roughly chop remaining 1/4 cup pistachios.
Remove sheet from oven; arrange strawberries on pistachio mixture, overlapping slices.
Brush berries and border with jam and sprinkle chopped pistachios on border.
