Parmesan Rosemary Focaccia Bread

1 medium onion, chopped
1/8 cup olive oil plus 3 tablespoons olive oil, divided
1 1/2 teaspoons active dry yeast
1 1/2 cups warm water (110 to 115 degrees), divided
1/2 teaspoon sugar
1/2 teaspoon salt
2 to 4 cups all-purpose flour
2 tablespoons snipped fresh rosemary or 2 teaspoons dried rosemary, crushed, divided.
A few tablespoons of Parmesan cheese

1) In a large skillet, saute onions in 1/8 cup oil until tender; cool. In a large mixing bowl, dissolve yeast in 1/4 cup warm water. Add sugar and let stand for 5 minutes.
2) Add 2 tablespoons oil, salt and remaining water. Add 2 cups flour. Beat until smooth. Stir in enough remaining flour to form a soft dough.
3) Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Add onions and half of the rosemary. Knead 1 minute longer. Place in a greased bowl, turning once to grease the top. Cover and let rise in a warm place until doubled, about 40 minutes.
4) Punch dough down. Turn onto a lightly floured surface; divide in half. Pat each piece flat. Let rest for 5 minutes. Grease two baking sheets and sprinkle with cornmeal. Stretch each portion of dough into a 10-in. circle on prepared pans. Cover and let rise until doubled, about 40 minutes. 5) Brush with remaining oil. Sprinkle with remaining rosemary and a few tablespoons of Parmesan cheese. Bake at 375 degrees for 25-30 minutes or until golden brown. Remove from pans to wire racks to cool.