Proof the yeast by combining the warm water, yeast and honey in a bowl. Stir and set aside for 10 minutes, by which time you should see significant foaming of the yeast as it expands. With instant yeast, this step isn't critical, as you can alternatively opt to combine all the ingredients of the entire recipe at the same time, but I like to proof even instant yeast to ensure its freshness before committing to the entire recipe.
Combine the flours and salt together in the bowl of standing mixer, and whisk a couple of times. Add the proofed yeast mixture and olive oil, and mix with the dough hook at the lowest speed for 2 minutes, or until the mixture begins to come together as a cohesive dough.
Spill the dough out onto a workspace and begin to knead together, adding whole wheat flour as needed if the dough becomes too sticky to work with. Continue to knead until the dough becomes soft and springy. Form the dough into a ball.
Oil a clean bowl, place the ball of dough in the bowl and cover with plastic. Place the bowl in a warm place of your kitchen to allow the dough to rise to double its size, about two hours. If it's a cold day, I place the bowl in my microwave oven with a cup of very hot water to allow it to rise, draft-free.
Preheat the oven to 500 degrees F with a baking stone on a rack placed in the middle of the oven.
Punch down the dough and divide it into eight equal pieces. I do this by weighing the total, and then dividing it by eight. Roll each piece into a ball, and flatten into a disk with your hand. Cover with plastic and let rest for 20 minutes.
Roll out each piece to a pita round 7 - 8 inches in diameter, using additional flour as needed to ensure the dough doesn't stick to the workspace surface. Make sure to roll the rolling pin over the edges of the dough to seal. Cover with plastic, and let the disks rest for another 10 minutes before baking.
Turn a baking sheet upside down and line with a piece of parchment paper. Place as many disks on the parchment paper as will fit directly on the baking stone. All surfaces of the dough must be in contact with the baking stone, and not drape over the side. Try to avoid overlapping the pita disks.
Bake for 3 minutes, or until the disks dramatically balloon. Remove and allow to cool. If you wait until the bread has browned, you will have a large, thick, crispy cracker instead of a soft pita round.
When the pitas are deflated, stack and serve slightly warm, or slice in half exposing the pockets. Stuff with filling such as scrambled eggs, roasted vegetables, or meatballs.
Pita bread rounds can be stored in ziplock bags in the refrigerator for one week.