Preheat the oven to 100 degrees F (38 degrees C).

Combine 1/2 cup lukewarm water with yeast and honey. Mix and set aside to proof, 5 to 10 minutes.

Combine both gluten-free flours in a stand mixer fitted with the dough hook. Turn mixer to low and while mixing, add oil and salt. Slowly add the yeast mixture; allow to mix. Add remaining lukewarm water, little by little, until all the flour comes together. Once a ball forms, knead on low speed for exactly 1 minute; the dough will be sticky but manageable.

Use your hands to form dough into a ball. Put it back into the mixing bowl and cover with a warm, damp towel. Turn off the oven and put the bowl in the warm oven. Let rise until almost doubled in size, about 45 minutes.

Use a kitchen scale and divide the dough into 6 equal balls. Cover again with the damp towel and return to the turned-off oven; let rise for 15 minutes.

Roll 1 dough ball between 2 sheets of parchment paper into a 6-inch round pita; avoid using flour or pitas will dry out or burn. Peel the parchment paper away from the dough.

Heat a cast iron griddle or comal pan over medium-high heat. Place the pita on the hot pan and cook until one side has browned slightly and begins to puff up, 2 to 3 minutes. Flip pita and cook until puffy on the other side, another 2 to 3 minutes. Use tongs to press down on the dough; it will continue to puff up.