Mash the butter into the flour in a mixing bowl with a pastry cutter or forks until it resembles small peas. Gradually add ice-cold water into the mixture, stirring lightly until the mixture is moist enough to form a ball. Place the pastry ball into a bowl and cover with plastic wrap. Mix almond paste, sugar, eggs, and almond extract in a separate bowl. Cover bowl with plastic wrap. Refrigerate both mixtures 8 hours to overnight.
Preheat oven to 400 degrees F (200 degrees C). Grease 2 baking sheets.
Divide the pastry into 10 portions. Using a rolling pin, roll each portion into long strips measuring about 4x12 inches. Divide the almond paste mixture into 10 portions; use your hands to form each portion into a snake shape. Place each almond 'snake' into the center of each pastry strip. Fold the dough over and seal the seam, also closing the ends. A little water will help to hold the seal. Arrange the rolls seam side down onto the baking sheets. Cut slits into the rolls with scissors every 2 inches.
Beat egg white and water together in a small bowl; brush over the pastry rolls to coat.
Bake in preheated oven until lightly browned, 20 to 25 minutes. Set aside to cool completely before slicing.
