1. In a large bowl, combine the flour, chilled butter, 1/4 cup sugar, and salt. Using a pastry cutter or your fingers, work the butter into the flour until the mixture resembles coarse crumbs.

2. Add the chilled milk and stir just until the dough comes together. Turn the dough out onto a lightly floured surface and knead briefly, about 30 seconds, until smooth.

3. Shape the dough into a disk, wrap in plastic wrap, and refrigerate for at least 2 hours or up to 3 days.

4. In a food processor, blend the pistachios and 1/2 cup sugar until a smooth, creamy paste forms. Transfer to a bowl and stir in the heavy cream and vanilla extract.

5. On a lightly floured surface, roll the chilled dough into a large rectangle, about 1/4-inch thick. Cut the dough into 12 triangles.

6. Place a heaping tablespoon of the pistachio cream onto the wide end of each triangle. Tightly roll up each triangle, starting from the wide end and working towards the point.

7. Place the rolled croissants seam-side down on a parchment-lined baking sheet. Cover and refrigerate for at least 30 minutes.

8. Preheat the oven to 400°F (200°C).

9. Brush the chilled croissants with the beaten egg. Bake for 18-22 minutes, until golden brown.

10. Allow the croissants to cool for 5 minutes before serving. Enjoy warm or at room temperature.