Reserve 1 tablespoon of the beaten egg; set aside. In a mixing bowl, beat together the remaining egg, almond paste, sugar, and flour until blended. Divide mixture in half. Shape each half into a 13-inch-long roll.
Roll out Butterdough to form a 14-inch square. Cut in half, forming two 14x7-inch rectangles. Place 1 of the almond-paste rolls on 1 rectangle of dough, positioned close to a long side of dough, leaving about 1/2 inch of dough at top and bottom of almond roll. Beginning at that long side, roll up dough, jelly-roll style, with the almond paste inside.
Transfer pastry to an ungreased baking sheet. Shape into a circle, joining ends; seal. Brush with reserved egg. Repeat with the remaining almond-paste roll and dough rectangle.
Bake in a 375 degree F oven for 30 to 35 minutes or until golden brown. Transfer to wire racks; cool. Ice and decorate pastry rings as desired. Makes 2 pastries (16 to 20 servings).
In a bowl, combine powdered sugar and water or milk.