In a large stoneware bowl, stir together the flours and salt. Make a well in the center of the flour mixture. Sprinkle the sugar and yeast into that well. Carefully pour the water into the well. Let stand until the yeast begins to act, about 5 minutes. Pour 2 tablespoons of the oil into the well. With a wooden spoon stir the mixture in the center of the bowl. Gradually widen the circle of stirring to take in all of the flour at the sides of the well.
Turn out on a floured surface, and knead just until smooth. Keep the dough soft. Pour 1/2 teaspoon of the oil into a clean bowl. Place the dough in the bowl, turning once to oil the top. Cover. Let rise until doubled, 30 to 45 minutes.
Punch the dough down. Use 1 teaspoon of the oil to coat a baking sheet, and place the dough on the baking sheet. Gently press the dough out to about 1/2 inch thickness. Pour the remaining 1 1/2 teaspoons oil over the top of the dough. Use the handle end of a wooden spoon to dimple the dough at 1 1/2 inch intervals. Sprinkle with the rosemary and the cheese. Place in a cold oven on the center shelf. Place a flat pan of hot water on the shelf below the bread. Let rise until doubled, 20 to 25 minutes.
Turn on the oven to 375 degrees F (190 degrees C). Bake the focaccia for 20 to 25 minutes, or until browned on top. Remove from the pan, and cool on a wire rack. Serve warm.