To make Lobster Fra Diavolo:
Bring a large 1-gallon pot of salted water to a boil, and place the pasta in the pot. Cook for 5 minutes and then drain; pasta will be only partially cooked. As the pasta cooks, set a large saute pan over medium-high heat and add the olive oil. Once the oil is hot, add the onions to the pan and cook until lightly caramelized and wilted, about 2 minutes. Add the shallots and garlic to the pan and saute until fragrant, about 30 seconds. Add the red pepper flakes and saute briefly before adding the tomato sauce and tomato paste. Cook the sauce until reduced by about half, about 5 minutes. Add the lobster to the pan and cook for 2 minutes. Add the partially cooked pasta to the pan along with 1 cup lobster stock and continue to cook the pasta in the sauce until al dente, about 3 to 4 minutes. Season the pasta with the salt and toss to combine. Garnish with fresh basil.
To make lobster stock:
In a large stockpot, heat the oil. Add the shells and stir. Cook for about 5 minutes. Add the celery, tomatoes, onion, carrot and thyme. Cut the fennel bulb in half and add to the pot. Cut the garlic head in half horizontally and add to the pot. Add enough water to cover the ingredients by about 2 inches. Season with salt and pepper. Bring the mixture to a boil, then reduce the heat and simmer until the liquid has reduced by half, about 4 hours.