In a large mixing bowl for a stand mixer, add water, yeast and honey. Let sit until bubbly.
Add olive oil, salt and 2 cups of flour. Mix on low speed.
Continue adding flour one cup at a time until all flour is incorporated.
Knead in stand mixer for 5 -10 minutes.
Shape dough into a round and place in a bowl greased with olive oil. Rotate the dough so all sides get coated with the oil. Cover bowl with plastic wrap or a clean dish towel. Let set for 1 hour or until dough has doubled in size.
Gently deflate the dough. Place dough on a lightly floured surface. Divide dough into fourths. Divide each fourth into three equal parts. You want 12 equally divided pieces of dough.
Shape each piece into a smooth ball. Place one piece of dough on the counter. Cup your hand over the dough. Rotate the dough in a circular motion with your hand until it becomes a smooth ball. Set aside and cover with a clean towel. Repeat with remaining pieces.
Roll out each piece of dough on a lightly floured surface to approximately 6 inches. Place each round on a lightly floured surface. Cover with a clean towel. Repeat with remaining dough.
Let dough rest for one hour. The dough will not rise very much during this time.
Preheat oven to 500 degrees Fahrenheit. Place a baking sheet on the bottom rack of the oven. This sheet will not be used for baking but helps create a barrier for the bottom of the bread so it doesn't become too brown.
Place four rounds of dough onto an ungreased baking sheet. Do not overlap dough. Bake for 5-6 minutes until lightly browned. Remove pitas to a baking rack and repeat with remaining dough.