Stage 1: Forge the Batter Foundation : In a medium bowl, sift the chickpea flour to remove any lumps. Add the ground flaxseed, kosher salt, dried oregano, minced rosemary, and black pepper. Whisk the dry ingredients together until thoroughly combined.
Stage 2: The Hydration Rest : Gradually pour the lukewarm water into the dry mixture while whisking continuously. Once a smooth, thin batter forms (the consistency of heavy cream), whisk in the 2 tablespoons of extra virgin olive oil. Cover the bowl and let the batter rest at room temperature for at least 1 hour. This allows the flour and flax to fully hydrate, which is crucial for the final texture.
Stage 3: Priming the Skillet : Twenty minutes before you plan to bake, place an oven rack approximately 6 inches from the broiler element. Place the 12-inch cast-iron skillet on the rack and preheat the oven to 500°F (260°C). A screaming-hot skillet is the key to a crispy socca base.
Stage 4: The High-Heat Sear : Five minutes before baking, switch the oven setting from 'Bake' to a high 'Broil'. Carefully remove the hot skillet from the oven using oven mitts and place it on a heatproof surface. Add about 2 teaspoons of the remaining olive oil and swirl to coat the bottom of the pan. Give the rested batter a final quick whisk and pour it into the center of the hot skillet. It should sizzle immediately. Tilt the pan to ensure the batter forms an even layer.
Stage 5: Broiler's Kiss : Immediately return the skillet to the oven rack. Broil for 7 to 10 minutes. Watch closely: the socca is done when the edges are crispy and pulling away from the sides, and the top is blistered with golden-brown spots.
Stage 6: Garnish and Serve : Using a wide metal spatula, carefully slide the finished socca from the skillet onto a cutting board. Drizzle with the last teaspoon of extra virgin olive oil and sprinkle generously with the za'atar. Slice into 6 wedges and serve immediately with fresh lemon wedges on the side for squeezing.