Soak the chickpeas overnight in water; drain. (Alternatively, use the quick-soak method: Place the chickpeas in a large pot with water to cover by 2 inches. Boil for 2 minutes. Remove from the heat and let sit for 1 hour, then drain.)
In a large saucepan, bring 3 qt. water and the soaked chickpeas to a boil. Add 4 cloves garlic and 2 bay leaves and cook until the chickpeas are tender, about 45 minutes. Drain, reserving 1 cup of the cooking water. Discard the bay leaves and let the chickpeas cool.
Using a food processor, puree the cooked chickpeas and garlic and reserved cooking water. Remove with a spatula and press through a mesh sieve.
Meanwhile, place the basil and remaining 2 cloves garlic in the food processor. With the machine on, drizzle in 1/2 cup EVOO and puree until well combined. Add the pine nuts and pulse until smooth. Add the chickpea puree, 1 tsp. salt and 1/2 tsp. pepper and blend all together.
In a medium saucepan, bring 6 cups water, the carrot, celery, onion and remaining 2 bay leaves to a boil; cook for 20 minutes. Add the shrimp and cook just until opaque, 1 to 2 minutes. Drain, discard the vegetables and let the shrimp cool. in a bowl, toss the shrimp with the remaining 3 tbsp. EVOO; season with salt and pepper.
To serve, spoon the chickpea puree onto a platter or individual plates and set the shrimp on top. Drizzle with the remaining oil from the tossed shrimp.