Instructions

for the dough

  Process flour and salt in food processor until combined, about 5 seconds. Scatter butter over top and pulse until mixture resembles coarse crumbs and butter pieces are about size of small peas, 6 to 8 pulses. Continue to pulse, adding 1 tablespoon ice water at a time, until dough begins to form small curds and holds together when pinched with fingers (dough will be crumbly), about 10 pulses.
 Turn dough crumbs onto lightly floured counter and gather into rectangular-shaped pile about 8 inches long and 3 inches wide, with short side facing you. Starting at farthest end, use heel of your hand to smear small amount of dough against counter. Continue to smear dough until all crumbs have been worked. Gather smeared crumbs together into another rectangular-shaped pile and repeat process. Divide dough in half and form each half into 3-inch disk. Wrap disks tightly in plastic wrap and refrigerate for 1 hour. Let chilled dough sit on counter to soften slightly, about 10 minutes, before rolling. (Wrapped dough can be refrigerated for up to 2 days or frozen for up to 2 months. If frozen, let dough thaw completely on counter before rolling.)
 Roll each disk of dough into 7-inch circle between 2 small sheets of floured parchment. (If dough sticks to parchment, gently loosen and lift sticky area with bench scraper and dust parchment with additional flour.) Slide dough circles, still between parchment sheets, onto rimmed baking sheet and refrigerate until firm, 15 to 30 minutes. (If refrigerated longer and dough is hard and brittle, let sit at room temperature until pliant.)

for the filling

  Adjust oven rack to lower-middle position and heat oven to 400 degrees. Gently toss peaches and blackberries and 2 tablespoons sugar together in bowl. (If fruit tastes tart, add up to 2 tablespoons more sugar.) Remove top sheet of parchment from each dough circle. Mound half of fruit in center of 1 circle, leaving 1½-inch border around edge of fruit. Being careful to leave ½-inch border of dough around edge of fruit, fold outermost 1 inch of dough over fruit, pleating it every 1 to 2 inches as needed; gently pinch pleated dough to secure, but do not press dough into fruit. Repeat with remaining fruit and dough circle.
 Working quickly, brush top and sides of dough with water and sprinkle tartlets evenly with remaining 1 tablespoon sugar. Bake until crust is deep golden brown and fruit is bubbling, 40 to 45 minutes, rotating sheet halfway through baking.
 Transfer tartlets with sheet to wire rack and let cool for 10 minutes, then use parchment to gently transfer tartlets to wire rack. Use metal spatula to loosen tartlets from parchment and remove parchment. Let tartlets cool on rack until juices have thickened, about 20 minutes; serve slightly warm or at room temperature.