Place sugar, yeast, and warm water in mixing bowl, let proof for 5-10 minutes or until yeast is foaming.
Add 2 T olive oil, then slowly add in white flour, 2 c whole wheat flour, and salt. Continue adding additional flour ½ c at a time and mixing until dough is pulling away from sides of the bowl and bowl is clean. Cover with a towel and let rest 30 minutes.
Knead dough for 5 minutes, form a ball. Drizzle ball of dough with remaining ½ t oil, cover with towel and let rise in the bowl in a warm, draft-free place for about an hour, or until doubled.
Gently punch the dough down, cover, and let rise again 20 minutes.
Prep 3 flat baking sheets with parchment paper. Lightly flour clean surface and divide dough into 12 balls, weighing balls if you can. Take each round and cup it with your hand.
Roll each dough ball with your cupped hand around and into the table, rotating it until it is a tight ball. Roll out with rolling pin until ¼" thick and place 4 on each baking sheet. Cover each baking sheet with towel and let rise 1 more hour, where each round is puffy.
Preheat oven to 450°F (230°C) and place rack on bottom level of the oven.
Bake each baking sheet of pita rounds about 4-5 minutes, or until puffed up and very lightly browned. Remove from baking sheet and wrap a stack in a towel.