It's all about the alliums in this eye-catching take on the Italian bread. Caramelized onions go into the dough, while leeks and chives are artfully arranged on top.
Add flour to the bowl of an electric mixer fitted with the dough hook attachment. In a liquid-measuring cup, stir together water and yeast until yeast is dissolved. Add yeast mixture to flour and mix on medium speed until combined. Cover with plastic wrap and let stand in a warm place until doubled in bulk and bubbling, about 2 hours.
In a large skillet, heat 2 tablespoons oil over medium-low. Add onions and slowly cook until dark golden and caramelized, about 45 minutes. Let cool.
Add salt and onions to dough and mix on low speed 5 minutes. Increase speed to medium and mix 30 seconds (dough should be loose and sticky).
Using a dough scraper, turn dough out onto a well-floured surface. Fold bottom edge of dough up toward center of dough and pat gently to deflate. Fold top edge down toward center, overlapping bottom edge slightly and pat gently. Repeat folding process 8 to 9 times, tapping off excess flour as you work (dough will be difficult to handle, but try not to incorporate too much flour). Gently transfer dough to a large bowl, seam-side down. Cover with plastic wrap and let stand in a warm place until doubled in volume, about 1 hour.
Turn dough out again onto a well-floured surface; repeat folding process. Return dough to bowl, cover with plastic wrap, and let stand in a warm place until doubled in volume, 1 hour more.
Place a pizza stone on floor of a gas oven with racks removed or bottom rack of an electric oven. Preheat oven to 450 degrees at least 45 minutes (425 degrees if using a convection oven).
Slice leeks lengthwise 1/4 inch thick. Rinse well and pat dry. Coat leeks, rosemary, and chives with 1 tablespoon oil.
Use remaining 1/3 cup oil to coat surface of a 13-by-17-inch rimmed baking sheet. Turn dough out onto sheet, coating bottom with oil. Using oiled fingertips, push dough out toward edges of sheet. If dough starts to retract, let stand 5 minutes, then continue until it reaches edges of sheet. Arrange leeks, chives, and rosemary lengthwise on dough, pressing gently to adhere. Cover with plastic wrap and let stand 45 minutes, occasionally pressing dough toward edges.
Liberally sprinkle dough with flaky salt. Dough should be well oiled; if necessary, drizzle with up to 2 tablespoons more oil.
Bake, rotating halfway through, until bottom is golden brown, 30 to 35 minutes. Immediately slide focaccia out of pan onto a wire rack. Drizzle with any reserved oil in pan and sprinkle with more flaky salt. Let cool slightly. Foccacia may be served warm or at room temperature.