Grease two large baking sheets; set aside. In a medium bowl combine chicken, cheese, and oregano.
Divide Master Dough into 16 portions. Roll or pat and gently stretch one portion into a 4-inch round. Spread 1 teaspoon of the hummus onto one side of the dough round. Top with a rounded tablespoon of the chicken mixture. Fold opposite side of the dough round over filling; seal edges with a fork. Transfer to a prepared baking sheet; prick top a few times with the fork. Repeat with the remaining dough portions, the remainder of the 1/3 cup hummus, and the remaining chicken mixture. Cover baking sheets with plastic wrap. Chill overnight.
The day of:
Let empanadas stand at room temperature for 20 minutes. Preheat oven to 400 degrees F. In a small bowl whisk together egg and the water. Brush over dough. Bake in the preheated oven for 15 to 20 minutes or until golden. Transfer to a storage container with a lid. Tote in an insulated carrier or wrap container in towels and place in a cooler (without ice). Serve within two hours with additional hummus.