Combine the onion and olive oil in a 4-quart saucepan; cook, stirring over low heat until tender, about 5 minutes. Stir in the broth. In a separate bowl, combine the water and cornmeal; stir into the broth and cook, stirring constantly, until the mixture boils and is very thick, about 10 minutes. Add cheese and salt, to taste.
Line a 13x9-inch baking pan with foil; spray foil lightly with olive oil cooking spray. Add the polenta and spread in a smooth layer with a spatula. Refrigerate until very cold and firm, about two hours. Turn polenta out of pan and peel off foil. Cut into 12 squares. Preheat oven to 425°F. Spray a nonstick-coated baking sheet with olive oil cooking spray. Arrange the polenta squares on the pan so that they are not touching.
Bake on bottom oven rack until browned on bottom, about 15 minutes. Turn and bake until browned and crisp, about 10 minutes more.
Meanwhile, cut peppers into 12 even portions and arrange on a platter. Drizzle with olive oil and sprinkle with herbs and a grinding of black pepper. Arrange on top of each polenta square. Serve warm or at room temperature.