Preheat oven to 350° F. Line three baking pans with parchment paper.
Working with one piece at a time, roll the dough on a floured surface into an 11 to 12-inch round about 1/8-inch thick. Top the dough with 3 tablespoons of apricot jam, spreading almost all the way to the edges. It will be thin.
Sprinkle 1/3 of the almond filling over the jam and spread it out evenly to cover the jam.
Using a pastry cutter or pizza wheel, cut the round into 16 equal wedges.
Starting at the wider outside edge, roll up the wedges into small crescents and place them on one of the prepared baking pans. Refrigerate for 15 minutes while you work with the next piece of dough.
Right before baking, brush the rugelach with the beaten egg and sprinkle generously with coarse sugar.
Bake the rugelach until pale golden and firm to the touch, about 25 to 30 minutes.
Transfer the hot cookies to a rack and cool briefly before eating.