makes 8; adapted from Sunset magazine
Measure water into a glass liquid measuring cup and sprinkle yeast over surface. Stir the yeast and let stand for a few minutes to proof. The yeast will get creamy and foamy.
In the work bowl of an electric mixer, add 3 3/4 cups flour, olive oil, honey, salt, and the yeast/water. Mix using the paddle attachment then switch to the dough hook and knead for 10 minutes. If the dough is still sticky, sprinkle in the remaining 1/4 cup flour (some or all depending on what your dough needs to get to be smooth and stretchy). If you don't have a dough hook, knead dough by hand but be careful not to add too much flour or the bread will be tough.
Lightly coat the inside of a large bowl with olive oil, add the dough, turn to coat, and cover with plastic wrap. Set aside to rise in a warm room temperature location, until doubled in size, about 45 minutes to 1 hour.
Turn dough out onto a lightly floured surface and cut into 8 equal pieces. Roll each into a ball, cover with plastic wrap or a clean kitchen towel, and let sit for 15–20 minutes so gluten can relax.
Position oven rack to lower-middle position, place baking stone on the rack, and heat to 425°F.
Alternatively, you can use a cast iron pan on the stovetop (medium-high heat), or an outdoor grill (brush one side of each round with olive oil then place pita round oil-side-down).
Using a lightly floured rolling pin, roll each ball into a 6–8 inch circle. Cook each for 4–5 minutes, flipping part way through the baking process, you want each side just beginning brown. Stack the cooked pitas on a plate or in a bread basket and cover with a clean kitchen towel to keep warm.