Whisk flour, water, and yeast with a mixer on medium speed until combined. Cover with plastic wrap, and let stand in a warm place until tripled in volume and bubbling, about 2 hours.

Add 1 tablespoon plus 1 1/2 teaspoons salt to bowl. Switch to dough-hook attachment, and mix on low speed for 5 minutes. Raise speed to medium, and mix for 30 seconds. (Dough should be loose and sticky.)

Turn out dough onto a well- floured surface using a dough scraper. Fold bottom edge of dough up toward the center, and pat gently to deflate. Fold top edge down toward the center, and pat gently. (Folds should overlap slightly.) Repeat with left and right sides, tapping off excess flour as you work. (Dough will be difficult to handle, but try not to incorporate too much flour.) Gently flip dough into a lightly floured bowl. Cover with plastic wrap, and let stand in a warm place until doubled in volume, about 1 hour.

Turn out dough onto a well-floured surface, and repeat folding process. Transfer dough to lightly floured bowl. Cover with plastic wrap, and let stand in a warm place until doubled in volume, about 1 hour.

Preheat oven to 450 degrees. Pour 1/3 cup oil onto a 13-by-17-inch rimmed baking sheet, coating entire surface. Turn out dough onto baking sheet, coating bottom with oil. Push dough out toward edges of baking sheet using your fingertips. Cover with plastic wrap, and let stand for 15 minutes, pressing dough toward edges occasionally.

Drizzle dough with remaining 2 tablespoons oil. Scatter cherries over top, and sprinkle with sugar and rosemary.

Bake in lower third of oven or on a pizza stone placed on the oven floor, rotating halfway through, until bottom is golden brown, 30 to 40 minutes. Immediately slide focaccia out of baking sheet onto a wire rack. Drizzle with any oil left in pan. Let cool slightly. Serve warm or at room temperature.