Combine the warm water, yeast and sugar in a small bowl. Put the bowl in a warm place, not hot or cool, until the yeast is bubbling and aromatic, at least 15 minutes.

In the bowl of a mixer fitted with a dough hook, combine the flour, 1 tablespoon of salt, 1/2 cup olive oil and the yeast mixture. Mix on low speed. Once the dough has come together, continue to knead for 5 to 6 minutes on medium speed until it becomes smooth and soft. Give it a sprinkle of flour if the dough is really sticky.

Transfer the dough to a clean, lightly floured surface, then knead it by hand 2-3 times. Again, give it another sprinkle or two of flour if the dough is really sticky.

Coat the inside of the mixer bowl lightly with olive oil and return the dough to the bowl. Cover it with a kitchen towel or plastic wrap and put it in a warm place until the dough has doubled in size, at least 1 hour.

Coat a medium sheet pan with the remaining 1/4 cup olive oil. Put the dough onto the sheet pan and begin pressing it out to fit the size of the pan. Turn the dough over to coat the other side with the olive oil. Continue to stretch the dough to fit all sides of the pan. Poke holes with your fingers. Cover with plastic wrap.

Put the dough in a warm place until it has doubled in size, about 1 hour. While the dough is rising a second time, preheat the oven to 425 degrees F.

Lightly drizzle a little oil on top of the focaccia and sprinkle the top with sea salt. Bake the focaccia until the top of the loaf is golden brown, about 25 minutes. Remove the focaccia from the oven and let it cool before cutting and serving.