How to Make Grilled Flatbread
Make the starter
Using your fingers, combine flour and yeast in a medium bowl. Make a well in center, and add 3/4 cup plus 2 tablespoons water. Blend with fingers until water is incorporated and there are no lumps (starter should be the consistency of thick pancake batter). Cover and let stand at room temperature until mixture is very bubbly and slightly risen, 12 to 18 hours.
Make the Dough
Using your fingers, combine flour, salt, and yeast in bowl of a heavy-duty stand mixer fitted with the dough hook attachment. Make a well in center; add flatbread starter and 13/4 cups warm water. Beat on low speed until ingredients are fully incorporated and dough starts to come together (dough will be very wet), 4 to 5 minutes. Let stand at room temperature 15 minutes.
Fold the Dough
Turn dough out onto a heavily floured surface. Gently press dough into a 1 -inch-thick oval. Starting with the side closest to you, fold dough over about two-thirds of the way to the opposite side; press gently. Fold far side about two-thirds of the way toward you; press gently. Rotate dough 90 degrees, and repeat folding procedure. Turn dough seam side down, and shape into a smooth ball.
Working with one piece of dough at a time, stretch dough over backs of hands (like shaping pizza dough) into an approximately 10-x 8-inch rectangle, and place on oiled grill grate. Work in batches; with practice, you may be able to manage shaping and grilling several dough rectangles at a time.
Return dough to mixer bowl, smooth side up, and let stand 15 minutes.
Turn dough out onto a heavily floured surface, and repeat Step 3. (Dough should now be elastic and smooth.) Return to bowl, smooth side up; cover and let stand until dough is doubled in size, about 2 hours.
Portion the Dough
Divide dough into 8 equal pieces (about 6 ounces each). Shape each piece into a ball. Cover with a clean dish towel, and let stand at room temperature 15 minutes.
Using fingertips, gently dimple dough balls, slightly flattening them into 4 -inch rounds. Transfer dough rounds to floured rimmed baking sheets so they can be transferred easily to the grill. Cover with a clean dish towel, and let stand 20 minutes. Meanwhile, preheat a grill or grill pan to high (450°F to 500°F). Using tongs, carefully wipe grill grate with a lightly oiled paper towel.
Grill dough rectangles, uncovered, until lightly charred on bottom, 1 to 2 minutes. (Wipe grill grate with oiled paper towels as needed between batches.) Flip dough rectangles, and grill until bottoms are well marked, 2 to 3 minutes. Remove from grill. Read on for our recommendations for finishing.