Mix the lukewarm water, honey or agave, and yeast in the bowl of a stand mixer. Let stand about 5 minutes.

Add both flours, salt, and olive oil. Mix a couple of minutes until the dough comes together.

Turn onto a lightly floured surface and knead about 5 minutes, until smooth and elastic, adding extra flour only if necessary.

Shape into a ball, place in an oiled bowl, cover, and let rise until doubled, about 1 hour.

Gently deflate and divide into 9 equal pieces. Shape each into a ball.

Roll each ball into a circle about 1/4 inch thick, lifting and turning as needed to prevent sticking. Cover the rounds with plastic wrap or a clean damp cloth.

Preheat oven to 450°F with a baking stone or baking sheet on the middle rack.

Bake 3 pitas at a time for 4–5 minutes, or until fully puffed. Repeat with remaining dough and cool before serving.