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Place the flour and salt in the bowl of a food processor and pulse a few times to blend the salt evenly into the flour.
Add the sugar and yeast to the water and stir. Allow the water-yeast mixture to sit for about 3 or 4 minutes and when foamy on top, add olive oil. Stir.
Turn on the processor and quickly pour the yeast-water through the feed tube. Process until the dough forms a ball. If the dough seems too wet, add more all-purpose flour, 1 teaspoon at a time. Remove from the food processor and form dough into a ball. Place in an oiled bowl and cover with plastic wrap. Let sit for 1 hour or until doubled in size.
Turn the dough onto a lightly floured surface and knead 2 or 3 times to remove any air bubbles. Form into a log and divide it evenly into 10 pieces. Form each piece into a ball and then roll into disks about 1/4 inch thick and 6 inches in diameter. Lightly oil two rimmed baking sheets. Put the disks on the baking sheets, cover with plastic wrap, and let rise an additional 20 minutes.
Prepare a medium-high gas grill fire, leaving one burner off, or prepare a charcoal fire with the coals pushed to either side of the grill, leaving an area in the middle with no coals underneath.
When very hot, place the pitas on the “cooler” part of the grill in batches and cook until starting to brown, 2 to 3 minutes. Depending on how hot your grill is, you may have to move the pitas directly over the heat for a few seconds to get them to brown properly, but be careful not to burn them. Flip and continue cooking until lightly golden on the bottom and the pitas are puffed and cooked through, 2 to 3 minutes more. Cool on a wire rack. If stuffing, cut the pitas in half and carefully separate the layers with a fork.
Nutrition information per pita:
Calories 210 Fat 3 g Sodium 360 mg
Carbohydrates 39 g Saturated fat 0 g Calcium 9 mg
Protein 5 g Cholesterol 0 mg Dietary fiber 2 g
Diabetic exchanges per serving: 2½ bread/starch, ½ fat.