In a medium bowl or a 4 cup measuring glass, whisk together the apple juice, water and yeast.  Set aside to proof. In a large mixing bowl add the flour, baking powder, extra virgin olive oil and salt.  Stir to combine. Add in the proofed yeast.   Using a dough hook, knead the dough in an electric mixer or knead by hand until the dough is completely blended.  Allow to rest for five minutes. Spray a large 13 or 14-inch pizza pan with nonstick spray.  Carefully pat the pizza dough onto the pan.  Make a ridge around the edge of the dough.   Completely cover the pizza crust with plastic wrap.  Smooth the crust by gently rubbing your hand over the plastic covered crust. Set the crust in a warm place, and allow to rise for 60 minutes. While the dough is rising preheat the oven to 400°F or 375°F convection bake.  Place a pizza stone in the oven.  Allow the pizza stone to completely heat through. Uncover the pizza crust.  Top with pizza sauce and (vegan) cheese. Place the pizza on the pizza stone and bake for 20 minutes until the crust is browned and the cheese is completely melted. Remove the pizza from the oven and allow to rest for 5 minutes before cutting.