Add the warm water, yeast and honey to the bowl of a stand mixer. (If you prefer, the dough can be mixed and kneaded by hand.) Stir gently. Set aside for 5 minutes until foamy.
Add olive oil, salt and 3 ¼ cups white whole wheat flour to the bowl. Using the paddle attachment, mix until combined. Switch to the dough hook and knead on low speed for 8 minutes, adding up to ¼ cup more flour if the dough is too sticky. The dough should feel only slightly sticky when you touch it with your finger.
Cover the bowl with a clean kitchen towel or plastic wrap and let rise for 45 minutes to 1 hour, until doubled in size.
If you are baking the pita on a baking stone in the oven, at this point you should place the baking stone in the oven and preheat oven to 500 degrees F. You can also bake the pita directly on the oven racks if you don’t have a baking stone. Or, bake them on a griddle, which I find to be easiest. (You’ll preheat the griddle right before baking as it doesn’t take as long to heat up as the baking stone.)
Transfer the dough to a lightly floured work surface and punch it down to release any air. Form dough into a ball and cut it into 10 equal pieces. Working with one dough piece at a time, gently shape it into a ball and then roll it into a 6-inch round on a lightly floured surface. Lay rounds on a sheet of parchment and cover with a clean kitchen towel.
Let dough rounds rest for 30 minutes. During this time they will puff up slightly.
Meanwhile, if you are baking the pita on a griddle rather than in the oven, preheat the griddle. I heat mine to between 350-375 degrees F.
Once dough rounds have rested, bake them 2 or 3 at a time, either in the oven or on the griddle. Bake on the first side for about 2 minutes, then flip and cook 1-2 minutes on the second side until lightly golden.
Let pitas cool slightly and then wrap loosely in a clean kitchen towel to finish cooling. This produces softer pita bread.
Store in a zip-top plastic bag at room temperature for 2 days or in the freezer for up to 3 months.