Add the garbanzo bean flour and 1 cup of water to a medium bowl. Whisk well and grate in 1 clove garlic with a microplane. Add 1 tbsp olive oil and ⅛ tsp salt. Whisk batter again to combine and set aside.
Rinse and dry the produce. Destem the Lacinato kale by holding the stem in one hand and stripping the leaves away with the other. Stack the leaves, roll, and slice into thin pieces. Thinly slice the broccoli florets.
In a food processor or blender, add the juice from half the lemon, basil, the remaining 2 cloves garlic, pumpkin seeds, ½ cup sliced kale, and a pinch of salt and pepper. Pulse a few times and drizzle in 2 tbsp olive oil, and then 2 tbsp water. Blend pesto on high until ingredients are well combined and texture is fairly smooth.
Place a large ovenproof nonstick skillet over high heat and add 1 tbsp olive oil. Once hot, whisk the batter again, add to the skillet, and tilt to cover the bottom. Cook, undisturbed, until batter begins to bubble and become firm, about 4 to 5 minutes. Transfer the skillet to the oven to broil until crisp on the bottom and slightly toasted on top, about 4 to 6 minutes.
Once the socca crust is browned on the edges, remove from the oven. Spread the pesto over the crust and top with remaining sliced kale, broccoli, and mozzarella. Return socca pizza to the oven until set and mozzarella has melted, about 4 to 5 minutes.
Cut remaining lemon half into wedges. Remove the socca pizza from the oven and transfer to a cutting board. Cut into 6 pieces and serve with lemon wedges.