Heat oven to 450 degrees. In a large mixing bowl, whisk together chickpea flour, salt, pepper, celery seed, fennel fronds and parsley. Slowly whisk in lukewarm water, making sure to eliminate all lumps. Stir in 2 tablespoons of olive oil. Fold in garlic and lemon zest. Let mixture sit and thicken for about 15 minutes (or up to 12 hours).
While socca thickens, make pesto: Bring a large pot of water to a boil. Blanch your nettles*: add leaves to a boiling pot of water for 1-2 minutes. Remove with tongs or a slotted spoon, and add to an ice bath to cool. Once greens are cool to the touch, strain and squeeze all water from the leaves. Roughly chop the blanched greens. Add to a food processor with garlic, pistachios, lemon juice and zest, parmigiano, salt and pepper. Pulse into a coarse paste. Then stream olive oil to desired consistency or about 1/3-1/2 cup. Set aside.
*NOTE: To de-stem your nettle leaves, hold onto stem with tongs, and use your other hand to carefully snip the leaves using kitchen scissors
Drizzle about 2 tablespoons of olive oil evenly into a cast iron (10-12 inches) or 9 x 11 baking dish to preheat for about 5-6 minutes (or until pan is very hot). Carefully remove hot pan and pour in batter evenly.
Top with sea salt, fresh pepper and bake for 12-15 minutes or until edges are browned and firm. If socca appears dry while baking or after, drizzle more olive oil over top. Let cool for 15-20 minutes. Then spread a thick layer of pesto over chickpea crust and dollop with burrata. Top with baby arugula, a sprinkling of pea shoots, flaky sea salt and freshly cracked pepper. Serve warm!