In large mixing bowl, combine yeast and sugar with 1 cup 110F water, stir to dissolve
Add whole wheat flour, 31g AP flour, and whisk together. Put bowl in warm (not hot) place, uncovered, until mixture is frothy and bubbling, ~15min
Set aside reserved 62g AP flour
Add salt, olive oil, 217g AP flour. With a wooden spoon or chopsticks, stir until mixture forms a shaggy mass. Dust with a little of the reserved AP flour and then knead in bowl for 1 minute, incorporating any stray bits of dry dough
Turn down onto work surface. Knead lightly for 2 more min until smooth. Cover and let rest for 10 min, then knead again for 2 min. Add reserved flour as needed, but only as required to continue kneading. You want to keep the dough soft and a bit moist
Put dough back into clean mixing bowl, cover tightly with plastic wrap and then a towel. Let rise until dough has doubled, about 1h
On bottom shelf of oven, place heavy-duty baking sheet or large cast-iron skillet. Preheat to 475F
Divide dough into 8 pieces. Form each into a ball. Place balls on work surface, cover with damp towel, and leave for 10 min
Remove one ball, keeping other covered. Press into flat disc with rolling pin. Roll into 8-inch circle, ~1/8th inch thick, dusting with reserved flour as necessary
Quickly place dough onto hot baking sheet. After 2 mins in the oven, flip the bread with tongs. Then bake for 1 more minute. Pita should be pale with only a few brown speckles. Transfer to a napkin-lined basket and cover to keep soft. Repeat with remaining dough balls