To prepare focaccia, lightly spoon flour into dry measuring cups; level with a knife. Place flour, sugar, salt, and yeast in a food processor; pulse 2 times or until blended. With processor running, slowly add very warm water through food chute; process until dough leaves sides of bowl and forms a ball. Process an additional 30 seconds. Turn dough out onto a lightly floured surface, and knead lightly 4 to 5 times. Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 30 minutes or until doubled in size.
Punch dough down; let rest 5 minutes. Roll into a 13 x 9-inch rectangle on a lightly floured surface. Transfer dough to a 13 x 9-inch baking pan coated with cooking spray; brush 1/2 teaspoon oil over dough. Cover and let rise 30 minutes or until puffy.
Preheat oven to 400°.
Uncover dough. Make indentations in top of dough using the handle of a wooden spoon or your fingertips. Sprinkle 1/3 cup green onions, Parmesan cheese, and 1/4 teaspoon pepper over dough, leaving a 1/2-inch border. Bake at 400° for 20 minutes or until lightly browned. Cool in pan on a wire rack.
To prepare sandwich, cut focaccia in half horizontally using a serrated knife; place bottom layer, cut side up, on a flat surface. Arrange provolone cheese and tomato slices over bottom layer; top with salad greens and 1/2 cup green onions. Combine balsamic vinegar and remaining ingredients in a small bowl, stirring well with a whisk. Drizzle vinaigrette over salad green mixture; top with remaining focaccia layer. Gently press sandwich together; cut into 6 equal portions.