Combine garbanzo flour and water in a bowl; whisk until batter is smooth. Cover bowl with plastic wrap or a plate and let stand at room temperature for 2 hours. Skim as much foam as possible from top of batter. Whisk salt, rosemary, and 3 tablespoons olive oil into batter.
Preheat oven to 500 degrees F (260 degrees C).
Place a 10-inch cast-iron skillet over high heat and heat until smoking hot. Pour 2 tablespoons olive oil in skillet and swirl to coat bottom of skillet with oil. Continue to heat until oil shimmers and a wisp of smoke rises from oil.
Quickly pour batter into hot oil; carefully transfer skillet to preheated oven.
Bake in the preheated oven until cake is browned and crusty, 25 to 30 minutes. Transfer immediately to a plate, cut into wedges, and serve hot. Garnish with freshly ground black pepper.