Whisk together the flour, salt, sugar, and yeast in a large bowl. Add the water and olive oil. Stir until no dry flour remains and the dough is thoroughly combined. Cover the bowl and allow the dough to rest for 15 minutes.
With a wet hand, grab one side of the dough, stretch it upward, and fold it into the center. Continue around the bowl 8 to 10 times until you've completed a full circle. Flip the dough over so the smooth side is facing up. Cover and rest for 15 minutes.
Repeat the stretch-and-fold process three more times at 15-minute intervals.
After the fourth stretch-and-fold, cover the bowl tightly and refrigerate for approximately 3 hours. Note: The dough may be refrigerated longer if desired. The cold fermentation adds flavor and provides flexibility in scheduling.
Remove the dough from the refrigerator and let it sit at room temperature for about 20 to 30 minutes.
Lightly oil the cavities of a 6-cavity bun pan.
Turn the dough onto a lightly oiled work surface.
Weigh the dough. It should weigh approximately 23.5 ounces (667 grams). Divide the dough into six equal portions, each weighing approximately 3.9 ounces (111 grams). Gently transfer each portion into a cavity of the prepared pan.
Cover the pan and allow the dough to rise at room temperature until puffy and relaxed, about 1½ hours at 74°F. The dough should feel soft and airy. A lightly oiled fingertip pressed into the dough should leave an indentation that slowly fills in.
Preheat the oven to 475°F.
Using one hand and oiled fingertips, gently dimple each bun several times. Lightly brush or drizzle olive oil over the tops of the buns. Sprinkle with flaky sea salt.
Bake for 7 minutes. Rotate the pan front to back. Continue baking for an additional 9 minutes, for a total bake time of 16 minutes.
Remove the buns from the oven and immediately remove them from the pan. Place the buns directly on the oven rack and bake for an additional 3 minutes to crisp the crust. Transfer to a wire rack to cool completely.
Yield: 6 Focaccia Buns