In the bowl of a stand mixer add yeast, sugar, and warm water (heated to 115°F). Allow mixture to sit for 10 to 15 minutes until foamy. Meanwhile, sift and whisk together the flours and salt in a separate large mixing bowl.
Mix the yeast mixture, olive oil, and ⅓ of the dry ingredients with the flat paddle mixture attachment at a medium-low speed until it forms a thick batter consistency. Switch to the dough hook on medium-low and add the remaining flour mixture until flour is well incorporated and forming a loose ball on the dough hook.
Transfer dough to a well-floured board and knead the dough for 7 to 8 minutes until the dough is firm, elastic, and holds its shape. Form dough into a ball and place into a large bowl oiled with olive oil. Cover with a warm, damp kitchen towel and allow to rise into a warm area of the kitchen for a minimum of 4 hours. Alternative: Tightly cover with plastic wrap and warm damp towel and refrigerate over-night, Remove the next morning and allow the dough to come to room temperature before continuing to the next step.
Place pizza stone onto a lower rack in the oven and preheat stone for at least 30 minutes at 450°F. In the meantime, punch down the dough and place the dough on a well-floured surface. Cut the dough into 8 equal pieces and form individual small balls, cover with a damp towel, allow to rest for 10 minutes.
Using a rolling pin roll out individual balls into 7-inch circles and flattened to a little less than ⅛-inch thick. Flour both sides of the pita dough and place it on the heated baking stone. Bake for 6 minutes until puffed, flip and continue baking for 2 more minutes until slightly browned in spots. Remove from the oven keep warm, wrapped in a kitchen towel. Repeat until all pitas are cooked. TIP: If your baking stone is big enough bake 2 - 3 pitas at a time.