1. Sprinkle the yeast and sugar over 1/2 cup of the warm water. Stir to dissolve. Let sit for about 10 minutes, until foamy.
2. In a mixer (I used my Kitchen Aid), use the paddle attachment to combine the remaining 1 cup of water, oil, salt, and 1 cup of the flour. Beat for 1 minute on medium speed, then stir in the yeast mixture. Beat in the rest of the flour and the chopped rosemary, 1/2 cup at a time, until the dough pulls away from the sides of the bowl.
Switch to the dough hook. Mix on low speed for about 3 minutes until the dough is stiff and sticky, adding 1 Tbsp. of flour at a time if the dough sticks. Place the dough into a deep oiled bowl, and turn it in the oil to coat it. Cover loosely with plastic wrap and let rise until doubled, about 1-1 1/2 hours.
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3. Once the dough has doubled, turn the grill onto medium-low heat. Divide the dough on a lightly floured board into half, and then divide each half into 5 equal pieces. Roll each piece into a ball. Let the dough balls rest for 10 minutes. You can roll out each ball, or form the rounds by hand. I prefer by hand. Each ball should be rolled into an approximately 6 inch round.
4. Place the rounds on the grill, and cover the lid. Check the bread frequently, as it will only take a couple minutes per side to puff up and cook. Flip the bread over and grill the other side, and then remove from the grill when the bread is puffy and looks completely baked. Stack the finished pitas on a plate and cover with a dish towel to keep warm while you grill the rest of the pitas.
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