Place flour, powdered sugar, butter, lemon zest, and salt, in a food processor. Pulse until the mixture resembles a coarse meal. Add the egg whites and process just until a uniform dough is obtained. If the dough is not coming together, add a little water (1-2 teaspoons).
Shape the dough into a disk about 1 inch thick before chilling. Wrap the dough in plastic wrap and transfer it to the refrigerator for 1 to 2 hours (up to overnight). Roll the dough on a floured surface to a ¼ -inch (½ cm) thickness and cut circles using a cookie cutter or a glass. Mix the raspberry jam with the cookie/cake crumbs. Place a flat teaspoon of the spread in the center of each circle.
Arrange the Hamantaschen on a baking sheet lined with parchment paper. Place the baking sheet in the freezer for 30 minutes to an hour before baking.
Preheat the oven to 350°F/180°C.
Bake for 15-20 minutes until the Hamantaschen is slightly golden. Let them cool.