Roll out pizza dough on a lightly floured surface with a floured rolling pin. Stretch gently with your hands and transfer to a large baking sheet or pizza pan sprayed with cooking spray.
Combine pizza sauce and barbecue sauce in a bowl and mix well. Spread evenly over pizza dough, leaving a 1-inch border.
Sprinkle on 1 cup mozzarella. Scatter ham and pineapple over top. Sprinkle on remaining 1 cup mozzarella.
Bake for 13-15 minutes, or until cheese is melted and golden brown. Sprinkle with green onions.