In a food processor, combine the flour, cold butter, egg, sugar, vanilla extract, and salt. Pulse until a dough forms. The mixture should resemble coarse crumbs before coming together.
Wrap the dough in plastic wrap and chill for 20–30 minutes. This will make it easier to roll out.
Once chilled, roll the dough out on a floured surface to about 3–4mm thickness. Use a round cookie cutter or glass to cut circles.
Place half of the dough circles on a parchment-lined baking sheet. Spoon a small amount of pistachio cream into the center of each circle.
Top with the remaining dough circles and gently press the edges to seal. Make sure the pistachio cream stays inside.
Brush the tops of the cookies lightly with milk, then sprinkle with granulated sugar and pistachio granules.
Bake in a preheated oven at 180°C (350°F) for 15 minutes, or until the edges are lightly golden. Allow to cool before serving.