In a large mixing bowl, cut butter into flour until pieces are the size of small peas. Sprinkle 1 tablespoon of the water over part of the mixture; gently toss with a fork. Push to side of bowl. Repeat until all is moistened. Form the dough into a ball and wrap in clear plastic wrap. Chill in refrigerator for 1 hour.
Meanwhile, crumble almond paste into a medium bowl. Stir in sugar and eggs. Let stand for 30 minutes.
Divide dough into 4 equal parts. On a lightly floured surface, roll each portion into a 13x8-inch rectangle. Cut each rectangle lengthwise into 2 equal strips, to make a total of eight 13x4-inch strips.
Stir almond-paste mixture until combined. Spoon almond mixture evenly down center of each pastry strip. Moisten edges of each pastry strip with water. Fold each long side over filling; seal edges. Pinch seams to seal into logs. Place seam-sides down on lightly greased baking sheets. Brush with the egg white mixed with 1 tablespoon water or just brush with the milk.
Bake in a 425 degree F oven for 10 minutes. Reduce oven temperature to 375 degree F. Bake logs for 10 minutes more or until light brown. Cool on wire racks. Cut each log crosswise into 4 pieces. Makes 32 pastries.