Preheat oven to 450 degrees. Combine yeast and water, and let stand until foamy, about 5 minutes. Stir well.
Pulse flour and 1 teaspoon salt in a food processor to combine. Add yeast mixture and oil. Process just until dough forms. Turn dough onto a lightly floured surface. Knead for 1 minute. Shape into a ball. Place in an oiled bowl, and turn to coat. Cover loosely with plastic wrap. Let rise until doubled, about 1 hour.
Punch dough. Divide into 4 pieces. Shape each piece into a 6-inch disk. Drizzle with oil. Sprinkle with salt. Place flatbreads on an inverted baking sheet.
Bake, without turning, until both sides of each flatbread are golden, 10 to 12 minutes. Let cool completely on sheets. Cut each flatbread in half crosswise.