At least 1 hour before making farinata, set a pizza stone on rack in upper third of oven and preheat oven to 550F.
Whisk together chick-pea flour and water until smooth, then whisk in salt and 2 tablespoons of oil. Let stand at least 30 minutes at room temperature.
Cook onion with salt to taste in 1 tablespoon oil in a large heavy skillet over moderate heat, stirring occasionally, until golden, about 10 minutes, then cool.
Put a seasoned 10-inch cast-iron round griddle on pizza stone and heat 10 minutes. Remove pan from oven and add 1/2 tablespoon oil, tilting to coat evenly. Working quickly, stir batter and ladle about 7/8 cup (1 cup minus 2 tablespoons) evenly into pan (batter will sizzle and start to set almost immediately). Quickly scatter a third of the onion, olives, and sage leaves over the batter and carefully return pan to pizza stone. If using an oven with a built-in broiler, bake 12 minutes, then turn oven setting to broil for 1 to 5 minutes. If using an oven with broiler underneath, bake 15 minutes, then transfer pan to broiler for 1 to 2 minutes. Edges should be golden brown and crisp and top flecked with golden spots.
Slide farinata onto a cutting board. Make 2 more in same manner, reheating pan 5 minutes for each successive farinata. Halve farinata and cut into strips.
Per serving: 558 Calories (kcal); 61g Total Fat; (96% calories from fat); 1g Protein; 5g Carbohydrate; 0mg Cholesterol; 2681mg Sodium Food Exchanges: 0 Grain(Starch); 0 Lean Meat; 1 Vegetable; 0 Fruit; 12 Fat; 0 Other Carbohydrates