How to Make It
Combine flour and yeast in a medium bowl with your fingers. Make a well in center, and add water. Blend by fingers until water is fully incorporated and there are no lumps (it should be the consistency of a thick pancake batter). Cover and let stand at room temperature until mixture is slightly bubbly and slightly risen, 12 to 18 hours.
Combine flour, salt, and yeast in bowl of a heavy-duty stand mixer with your fingers. Make a well in center; add Flatbread Starter and warm water. Using dough hook attachment, beat on low speed until ingredients are fully incorporated and dough starts to come together (the dough will be very wet), 4 to 5 minutes. Let stand at room temperature 15 minutes.
Using a bowl scraper or spatula, turn dough out onto a heavily floured surface. Gently press dough out until slightly flattened. Starting with the side closest to you, fold dough over about two-thirds of the way to the opposite side, pressing gently. Then fold the side furthest away from you over about two-thirds of the way to the side closest to you, pressing gently. Rotate dough piece 90º, and repeat folding procedure with the 2 unfolded sides. Turn dough seam side down, and shape into a smooth ball.
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. (The dough should now be elastic and smooth.) Return to bowl, smooth side up; cover and let stand until doubled in size, about 2 hours.
Divide Flatbread Dough into 8 equal pieces, about 6 1/8 oz. each. Shape each piece into a ball. Cover with a clean dish towel, and let stand at room temperature 15 minutes.
Meanwhile, preheat a grill to high (450°F to 500°F). Using tongs, carefully wipe grill grates with a lightly oiled paper towel. Using a grill brush, scrape grates clean, then wipe with an oiled paper towel once more.
Using your fingertips, press each dough ball into a rectangular shape; stretch each piece into a 6-inch circle. Arrange dough circles on a cutting board or a baking sheet sprinkled with flour. Cover with a clean tea towel, and let stand 20 minutes. (This final proofing builds more air into the dough, creating its chewier, fluffier texture.)
Shape each dough circle into a 10- x 8-inch rectangle. Transfer dough rectangles, in batches, to oiled grill grate, and grill, covered, 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.