Prepare socca batter at least 30-60 minutes ahead of time, preferably several hours or overnight. Sift the chickpea flour into a mixing bowl. Add the water, olive oil, garlic, and sea salt. Whisk until smooth. Cover and let sit at room temperature until ready to bake, or refrigerate if preparing the day before.

Prepare chimichurri. Place cilantro, parsley, shallot, and garlic into a food processor and pulse until the finely chopped. Alternatively, chop the herbs, shallot, and garlic with a chef's knife. Transfer the herbs to a bowl. Stir in 6 tablespoons olive oil, lemon juice, vinegar, sea salt, and red pepper flakes. Taste and adjust seasonings as needed. If the chimichurri is too thick, add the extra olive oil. Cover and refrigerate until ready to serve.

To cook the socca, remove the batter from fridge and bring to room temperature. Place oven rack about 5" from the broiler and preheat broiler for 10 minutes. Place a well-seasoned cast-iron skillet or two 8-inch round metal cake pans into the oven. Let heat for 5 minutes. Open oven door and slide rack out. Add 2 tablespoons olive oil to the cast-iron skillet. Swirl gently, being careful because the pan will be fiery hot. Pour the batter into the pan and tilt so the batter fills the pan to the edges. Place in oven and broil for 6-8 minutes, or until the edges are crispy, the center is set, and the top is golden.

Meanwhile, line a baking sheet with parchment paper and get the toppings ready. When the socca has baked, remove it from the pan and place it on the baking sheet. Adjust oven temperature to 425°F. Sprinkle a little of the fresh mozzarella evenly over the socca, followed by the squash, and tomatoes. Top with remaining mozzarella, crumbled feta, and a good sprinkle of freshly ground black pepper and sea salt. Place pan in oven and bake for 15-20 minutes, or until the cheese is golden and melty. (If you want the top to be extra toasty, place the socca back under the broiler for a minute or two, watching carefully so it doesn't burn.)

Before serving, drizzle with chimichurri, and cut into wedges. Serve warm or at room temperature.