Heat oven to 400° F. In a small saucepan, combine the apricots and 1/2 cup of water and bring to a boil. Remove from heat, cover, and let stand 5 minutes. Remove the apricots from the water, let cool, and coarsely chop.
On a lightly floured surface, cut the sheet of puff pastry lengthwise into thirds, and cut each third in half (for six 4-by-6-inch pieces). Place 1 teaspoon of the preserves in the lower center of each piece of dough. Top with the chocolate chips and chopped apricots. Brush the edge of each pastry with egg and fold the pastry over the filling, pressing the edges together. Using the tines of a fork, seal the packets securely and brush the tops with the remaining egg. Sprinkle each with 1 teaspoon of sugar. Place the pastries on a cookie sheet lightly coated with vegetable cooking spray and bake 25 to 30 minutes, or until golden brown. In a small bowl, combine the ground coffee with the remaining sugar. Serve the Pastry Pillows warm or at room temperature with the ice cream sprinkled with coffee sugar.