Directions

1. Fill sink with ice water. In a stockpot, combine onion, carrot, bay leaves, garlic, ginger, zest, and peppercorns with 8 cups water; cover and bring to a boil. Add lobsters, cover, and cook 8 minutes once water has returned to a boil. Remove lobsters, reserving the liquid; transfer to the ice bath.
2. When lobsters are cool enough to handle, break tails and claws from body; crack open to remove meat. Set meat aside. Add bodies and empty shells to reserved liquid; return to a boil. Reduce heat; simmer 30 minutes. Drain through a fine sieve; discard solids. Return liquid to pot; cook over medium-high heat until reduced to 1 cup, about 45 minutes. Cut meat from lobster-tail and claw into bite-size pieces; set aside.
3. Bring a 5-quart saucepan of salted water to a boil, and cook pasta until al dente, about 7 minutes. Drain in a colander, and set aside.
4. Cut onion into 1/8-inch wedges; remove the core. Cut zucchini lengthwise into quarters and crosswise into 1/2-inch pieces. Heat a low-sided 6-quart saucepan coated with olive-oil cooking spray over medium-high heat until very hot. Add onion and garlic; reduce heat to medium low. Cook until onions are translucent, about 3 minutes. Add zucchini; cook until tender, about 7 minutes. Add corn, reserved lobster meat, cooked pasta, reserved liquid, arugula, and marjoram; stir to combine. Stir in Parmesan, if desired; serve.