Preheat the oven to 500 degrees F and place an 8-inch cast iron skillet on the top oven rack to heat up.
Whisk the chickpea flour and salt together in a medium bowl, then slowly stream in the water as you whisk. Continue whisking until smooth, then whisk in 1 tablespoon of olive oil. Set the batter aside to rest as the oven heats up.
When the oven is heated, remove the pan and add the remaining olive oil, swirling it around to coat the entire pan. Pour the batter over the hot oil and give it another swirl to cover the entire bottom. If needed, you can spread the batter out with a spatula so that it’s even in the pan.
Place the pan on the top rack of the oven and then turn on the broiler, keeping the oven door cracked to prevent the oven from cycling off. When the farinata is golden brown and slightly charred on top, around 5-10 minutes, it's done – keep a close eye on it as it cooks quickly.
Slice into wedges and serve immediately.