Measure out the warm water and stir in the sugar until it is dissolved. Add the yeast, stir lightly, and let sit for 15 minutes in a warm place.

In a large bowl, stir together the flour and 1 tablespoon of kosher salt.

When the yeast has proofed, add it to the flour along with 1/2 cup of olive oil. Stir with a wooden spoon until the dough comes together.

Transfer the dough to a clean surface and kneed until it becomes smooth (a few minutes).

Coat the bowl lightly in olive oil and return the dough to the bowl. Cover the bowl and let the dough rise in a warm place for about an hour or until doubled.

Pour 1/4 cup of olive oil into a large jelly roll pan. If you need a bit more to have a generous coat over the entire surface of the pan, add a bit more.

When the dough is done with its first rising, flatten it out into the pan.

Begin pressing down on the dough with the pads of your index, middle, and ring fingers. Use this process to slowly stretch the dough out to the size of the pan. 

Flip the dough once or twice during the dimpling process to coat thoroughly in olive oil. Do not be afraid to make deep imprints and even poke through the dough entirely. 

When you are done, set the pan in a warm place to rise again for 1 hour.

While it is rising, mix the brine. Measure out 2 tablespoons of warm water and 1 teaspoon of salt and whisk together in a bowl. Add to this 2 tablespoons of olive oil and whisk thoroughly.

Preheat the oven to 425F and brush the top of the dough with the brine, using all of it. 

Sprinkle with coarse sea salt and bake for about 25 minutes or until it is a golden brown.

Cut immediately and serve.