Beat almond paste, butter, and sugar in a small bowl until smooth and well blended.
Roll dough on floured surface to a 30" x 9" rectangle; cut lengthwise into three strips. Spread filling down center of each strip, dividing evenly. Fold edges of strips over filling to enclose filling completely. Press ends of the three filled strips together; braid; press other ends of strips together.
Ease braid onto an ungreased cookie sheet. Join ends together to make a ring, about 9" in diameter. Let rise in a warm place 45 minutes or until doubled in bulk. Brush with egg Sprinkle generously with sugar and almonds. Place in a hot (400f) oven; lower heat immediately to 350f. Bake 40 minutes or until puffed and golden; remove to wire rack; cool. Cut into wedges to serve. This cake is rich and will spread when baked. You may want to place a collar of foil around it just before baking to keep it more compact.