For the dough, dissolve the yeast in 1/2 cup warm water in a medium bowl. Stir in 1-1/4 cups water and 2 tablespoons of the olive oil.

Pulse the flour and salt together in the bowl of a food processor. Add the yeast mixture and process until a rough ball of dough forms, 1 minute. Briefly knead dough on a floured surface until smooth. Shape dough into a ball. Put 2 tablespoons of the oil into a large bowl. Roll dough around in bowl until coated with oil. Cover the bowl with plastic wrap and let the dough rise in a warm spot until it has doubled in size, about 2 hours.

Pour a thin film of oil into each of four 8-inch round cake pans. Quarter the dough and put one piece into each pan. Using your fingertips, spread dough out in each pan. The dough is elastic and will resist stretching. Let it relax for 5 minutes or so after you've stretched it as far as it will go. Eventually, it will cooperate and fill the pan.

Preheat the oven to 450°. Cover the pans with damp dishcloths and let the dough rest until it has swollen in the pans a bit, 30-60 minutes.

Uncover the pans. Sprinkle the dough with the rosemary. Using your fingertips, poke dimples into the dough in each pan, then liberally drizzle with oil so it pools in the hollows. Arrange just the thinnest rounds of lemon on top, drizzle with more oil, and sprinkle with sea salt. We like ours salty. Bake the focaccia until golden brown, 20-30 minutes. Drizzle with more oil when you pull the focaccia from the oven. Serve cut into wedges.