For the lobster stock:
In a large stockpot filled with boiling water, cook the lobsters for approximately 8 minutes. Drain, remove and de-shell the lobsters, keeping the carcasses for the stock. Reserve the lobster meat in a separate bowl for later.
In the same stockpot, add the oil. Combine the lobster shells with the carrot, celery, onion, garlic, rosemary, thyme, peppercorns, water, and ketchup. Bring the mixture to a simmer and let reduce for 2 hours. Strain and transfer 6 cups/1.5 L of the remaining stock into a smaller saucepan, reducing on medium heat for another 20 minutes or until approximately 1/3 of the stock is left. Remove from the heat and set aside.
Bring a pot of salted water to a boil and add the fettuccine. Cook 1 minute less than instructed. Strain and set aside.
Heat 1 tablespoon olive oil in a pan on medium heat and add the shallot. Saute 1 minute, then add the garlic and continue cooking for another 2 minutes. Add stock. Add the pasta, reserved lobster meat, peas, and chives, and 2 tablespoons butter and mix well. Salt, and pepper, to taste.
Cook's Note: Any leftover lobster stock can be kept in the freezer for up to 3 months.