Preheat oven to 400 degrees F and line a large baking sheet with parchment paper; set aside. On a lightly floured surface, roll each pastry sheet out to approximately a 10×10-inch square. Using 3-inch round cookie cutters, cut 13 circles into each pastry sheet. On one sheet, cut 1-inch circles (or similarly sized shape) into the centers of the larger circles. Remove the center circles.
Place the intact circles onto the prepared baking sheet and brush surfaces with the beaten egg. Place 1/2 teaspoon of the raspberry jam into the center of each. Top with the remaining circles (with centers cut out) and brush with the egg. Spread the jam to fill the center hole. Sprinkle sugar over the tops. Bake in the preheated oven for 12-15 minutes, or until golden brown on tops and sides and donuts are puffed up to at least 1 inch high. Let cool.
MAKE THE ICING
Place the freeze dried raspberries in a coffee grinder or small food processor and grind into a powder. Using a stand mixer fitted with the whisk attachment (or a large mixing bowl with a hand mixer), combine the confectioner’s sugar and raspberry powder. Add the milk 1 Tbsp at a time until desired consistency is reached. Beat on medium speed until free of lumps.
ASSEMBLE THE COOKIES
Dunk the tops and sides of the donuts into the glaze. Place on serving tray and serve immediately!