Combine water, yeast, honey and olive oil. and let sit while mixing flour. In a separate medium sized bowl, combine 3 3/4 cups bread flour, rye flour and salt. Using a rubber spatula, slowly pour in the yeast mixture, stirring to combine.
At this point you have 1 1/2 cups of bread flour remaining. Pour this flour out onto a clean work surface. Turn dough out into the center of the pile of remaining and flour and begin to knead this flour into the dough. Fold the dough in half towards you, and then push dough away from you with the heels of your hand. Turn dough a quarter turn, and repeat kneading. Knead till dough is smooth, and the flour has been incorporated into the dough, about 8 minutes.
Place dough in a clean floured bowl, cover with plastic wrap and let rise in a warm location until doubled in size, about 1 hour to 1 hour and 30 minutes.
Remove dough from bowl and knead for about a minute. Divide dough into 8 –10 equal portions. Shape pieces into balls, but don't overwork. Place on a floured sheet pan, cover and let sit in a warm place for 30 minutes.
Preheat oven to 500°Place a baking stone* in oven while oven preheats.
Using a rolling pin, roll dough balls into circles, about 8" across and about 1/8” thick. Transfer the dough one or two at a time to the hot stone. Bake for about 3-5 minutes, watching carefully. They will poof up and brown lightly. If you'd like these pitas not to have a "pocket", dock the dough rounds before baking by poking lightly with a fork across the surface of the round. This will make the bread remain thicker and pocketless.
These dough rounds will keep in the freezer for about a month. Let cool thoroughly and then place in a zip top bag. I like to warm them in a skillet with a bit of olive oil or you can warm on a sheet pan in the oven.