Mix 1 cup of the flour, the sugar, salt and yeast in large bowl. Add 1/4 cup oil and the warm water. Beat with electric mixer on medium speed 3 minutes, scraping bowl occasionally. Stir in enough remaining flour until dough is soft and leaves side of bowl.
Turn dough onto lightly floured surface. Knead 5 to 10 minutes or until dough is smooth and elastic. Place in greased bowl; turn greased side up. Cover and let rise in warm place 1 to 1 1/2 hours or until double. (Dough is ready if indentation remains when touched.)
Heat oven to 425º. Grease 2 cookie sheets. Punch down dough. Divide in half. Shape each half into flattened 12-inch round on cookie sheet. Cover and let rise in warm place 20 minutes.
Meanwhile, heat 2 tablespoons oil in 10-inch skillet over medium heat. Cook bell peppers and onions in oil, stirring occasionally, until tender.
Prick centers of focaccias and 1 inch in from edges thoroughly with fork. Brush with 1 to 2 tablespoons oil. Spread bell pepper mixture over focaccias. Sprinkle each with 1 tablespoon herb leaves and cheese. Bake 12 to 15 minutes or until golden brown. Serve warm.