In the work bowl of a food processor, pulse confectioners’ sugar and almond flour until combined. Add egg whites and almond extract; pulse until a somewhat smooth dough forms and mixture is combined. Turn out mixture onto a clean surface, and gently knead a few times until dough is smooth. Cover until ready to use, or wrap tightly in plastic wrap, and refrigerate for up to 6 weeks.

Preheat oven to 350°F (180°C). Line rimmed baking sheets with parchment paper.

Divide almond paste into 4 pieces (about 161 grams each.) Dust a sheet of parchment paper with confectioners’ sugar; add one portion of almond paste. Dust with confectioners’ sugar, and top with another sheet of parchment paper. Press and roll almond paste into a 9-inch circle. (Keep remaining almond paste covered until ready to use.)

Divide Rugelach Dough into 4 portions (about 181 grams each). On a work surface lightly dusted with all-purpose flour, roll one portion of dough into a 10-inch circle. (Keep remaining dough refrigerated until ready to use.) Remove top parchment from almond paste, and invert onto dough. Remove top parchment. Spread ¼ cup preserves (about 80 grams) onto almond paste. Using a sharp knife or pastry cutter, cut dough into 12 triangles. Starting at base of each triangle, roll up triangle toward point, and place 1½ inches apart on prepared pans. Repeat procedure with remaining almond paste, remaining dough, and remaining preserves.

In a small bowl, whisk together egg and 1 tablespoon (15 grams) water; brush onto dough, and sprinkle with sparkling sugar.

Bake until golden brown, 20 to 25 minutes. Let cool completely on pans on wire racks. Store in an airtight container for up to 5 days.