Preheat oven to 450 degrees fahrenheit. Add an empty 10-inch cast-iron pan into the oven and heat for 10 minutes.
In a mixing bowl, whisk together the chickpea flour, water, salt and pepper, removing all clumps and forming a thin batter. Set aside.
In a small sauté pan, heat 1 1/2 tablespoons of olive oil on medium heat. Add the garlic and shallot and sauté for one minute, until translucent.
Pour the entire contents of the sauté pan (garlic, shallot and oil) into the batter and whisk again.
Wearing oven mitts, carefully remove the cast-iron pan from the oven. Swirl 1 1/2 tablespoons of olive oil into the pan, coating the bottom, then pour the socca batter into the pan, swirling until the batter reaches the edges of the pan. Place the pan back in the oven and cook for 12 minutes, until golden.
While the batter is cooking, make the salad by gently tossing the pear, arugula, olive oil and lemon juice together in a bowl.
Carefully remove the socca from the oven and use a spatula to transfer it to a paper towel to blot dry. Place the socca on a plate and top with the salad, shaved parmesan, salt and pepper.