Remove one dough sheet from the fridge and place on work surface. Peel off top parchment sheet and gently lay it back in place. Flip the dough over; peel off and set top parchment layer aside. Use a 3-inch round cookie cutter (or upside-down glass) to stamp out as many rounds as possible, leaving as little space between them as possible so that you do not have too many scraps. Place rounds on parchment lined baking sheet, setting them 1½ inches apart. Set scraps aside.
Brush the edge of the circles with water. Spoon about 1 Tablespoon of the pistachio filling into the center of each circle. Fold up three sides of the dough against the filling, forming a triangular shape. Pinch the edges and corners firmly so that the shape holds together. Repeat with remaining filling and dough. Scraps can be rerolled and chilled for at least 30 minutes before cutting and baking more hamentashen
Preheat oven to 350°F. Chill unbaked hamentashen for about 30 minutes before baking. It will prevent the hamentashen from slumping and they will hold their shape much better. Brush chilled hamentashen with egg white.
Before baking, add a second baking sheet under chilled hamentashen. The double baking sheets will prevent the bottom of the hamentashen from getting too brown, before the tops and sides are done. Bake the hamentashen, rotating baking sheet halfway through, until golden, 16-18 minutes. Let cool completely.
Place milk chocolate into a medium sized heatproof bowl. Microwave on 50% power for 15 seconds. Stir and continue heating in additional 10-15 second bursts, until completely melted.
Dip hamentashen into melted milk chocolate. Sprinkle on some chopped pistachios. Chill until chocolate is firm. Hamentashen should be stored in an airtight container for 5 days or frozen for up to a month.