Combine the yeast and warm water in a bowl, add 3 tablespoons olive oil to the water and let soak for 5 minutes. Mix the flour, 1 tablespoon salt and half the rosemary together in a bowl. Using a wooden spoon, pour the water yeast mixture into the flour and stir together to form a well mixed dough. Scrap the dough out onto a floured work surface and begin to work the dough with the heel of your hands, pulling and folding the dough as you push and pull.
Work the dough for 10 minutes, put the dough into a lightly oiled bowl and then let rise at room temperature for 1 1/2 hours. Lightly oil a cookie sheet pan, spread the dough out in the pan and pull the dough evenly into the corners. Let the dough rise again for 1 hour more. Poke the surface of the dough with the tip of a your finger and drizzle the remaining olive oil over the surface of the dough, sprinkle with the coarse salt and remaining rosemary and bake at 450 degrees for 20 minutes. Check the bottom of the focaccia to ensure it is not burning and bake an additional 5 minutes.