In a large bowl, combine 1 cup flour, sugar, yeast and salt. Add warm water and shortening. Beat on medium speed for 2 minutes. Add 1/2 cup flour; beat 2 minutes longer. Stir in enough remaining flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 45 minutes. Punch dough down. Cover and refrigerate for 2 hours.
Turn dough onto a lightly floured surface; roll into a 15x10-in. rectangle. In a small bowl, beat cold butter until softened but still cold. Spread dough with a fourth of the butter. Fold dough into thirds, starting with a short side. Turn dough a quarter turn. Repeat rolling, buttering and folding three times. Wrap in plastic. Refrigerate overnight.
On a floured surface, roll dough into a 14-in. square. With a sharp knife, cut into quarters. Cut each quarter diagonally in half, forming two triangles. Roll up triangles from the wide end; place with pointed end down 2 in. apart on a greased baking sheet. Curve ends to form a crescent shape. Cover and refrigerate for 20 minutes.
Brush with egg. Bake at 425° for 13-18 minutes or until golden brown. Remove from pan to a wire rack to cool.