In a medium bowl, whisk the flour and salt. Make a well in the center and pour in the water and oil. Using your fingers, draw the flour in from the sides, working the mixture into a sticky dough. Turn the dough out onto a floured surface and knead, adding more flour as necessary to prevent sticking, until the dough is smooth and elastic, about 3 minutes. Transfer to the mixing bowl, drizzle with a little bit of oil, and turn to coat. Cover the dough with plastic wrap and let rest at room temperature for 4 hours or refrigerate overnight.
On a floured surface, divide the dough into 6 equal pieces (about 2 oz. each). Roll each piece into a ball. Cover the dough balls with a clean kitchen towel and let rest at room temperature for 15 minutes.
Cut seven 10-inch squares of parchment. On a floured surface with a lightly floured rolling pin, roll the balls into very thin 9-inch rounds, using more flour as needed to prevent sticking. (If the dough resists rolling, let it rest for another 15 minutes.) Layer the rounds between pieces of parchment in a stack.
Heat an 11- to 12-inch nonstick or cast-iron skillet or griddle over medium heat. Lightly oil the skillet. Peel a dough round from the parchment and drop it into the skillet, carefully using your fingertips to lay it flat, if necessary. Cook until light golden and puffed in spots, about 2 minutes. Using your fingers or a spatula, flip and cook until the second side is light golden in spots, 1 to 2 minutes. Transfer to a plate. Repeat with the remaining dough, stacking the cooked flatbreads so they steam a bit and stay warm.
If not using immediately, transfer the warm yufka to a large zip-top plastic bag, close it, and store at room temperature overnight. You can also freeze the yufka for up to 2 weeks. Reheat briefly in a skillet over medium heat before using.