Add all ingredients to a mixing bowl in the order listed. Use a dough hook attachment on a stand mixer to knead on medium speed for about five minutes until smooth.
Cover the dough tightly and refrigerate for at least 24 hours (up to 4 days) to develop flavor and improve texture.
Preheat the oven to 450°F (232°C) and position a baking steel, stone, or an overturned baking sheet on the lowest rack.
Lightly flour a work surface with gluten-free flour and knead the chilled dough until smooth. Divide into 8 equal portions (about 95 grams each) and roll into balls.
Coat each dough ball with gluten-free flour and roll into 6-inch diameter circles (no more than ¼ inch thick).
Transfer two rolled pitas at a time onto the hot baking surface. Bake for 2 minutes, then flip and bake for an additional 2-3 minutes until puffed and golden.
Remove from the oven and brush each side with butter while warm. Cover with a paper towel and a kitchen towel to keep soft.
For a smoky flavor, grill the pita on high heat for 2-3 minutes on each side instead of baking.
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Notes
Store baked pita in an airtight container or zip-top bag at room temperature for up to 5 days. For longer storage, freeze individually wrapped pitas.