Season pork shoulder with spices and salt and pepper. Place in baking dish and pour root beer around the sides. Slow roast in oven at 325 degrees F for about 3 1/2 to 4 hours, or until pork is tender and falls off the bone.
Shred pork and mix in the BBQ sauce. Set aside.
Heat oven to 375 degrees F. Place pie crust dough on a lightly flour surface. Cut out round discs. Place a small amount of pork filling in the center of each round. Be sure not to overfill. Fold dough in half to form a half circle. Press edges together to seal, and work from one end to another, creating pleats. Place on a greased parchment lined baking sheet.
Mix egg with 2 tablespoons water. Brush the egg wash on the surfaces. Bake for about 20-25 minutes or until golden brown.