In a bowl, combine the 1 cup (4 oz/125 g) flour, 1 cup (8 fl oz/250 ml) room temperature water, 2 tablespoons olive oil, the rosemary, ¾ teaspoon salt, and a generous amount of pepper. Whisk until smooth. Use right away or cover and let stand at room temperature for 30 minutes to 2 hours, or refrigerate overnight.
Arrange the rack in the top part of the oven and preheat to 500°F (260°C). After the oven is fully heated, turn on the broiler, place two 9-inch cake pans in the oven, and heat for 2 minutes. Carefully remove the hot pans from the oven, pour 1 tablespoon oil into each, and swirl to coat the bottoms. Return the pans to the oven until the oil is just smoking, about 2 minutes longer. Carefully remove the pans from the oven and divide the batter between the pans, swirling to cover. Broil until the socca are firm and deeply browned in spots, watching carefully, 7–12 minutes. Serve right away.