Place the live lobsters in the freezer for about 30 minutes. This numbs the lobsters, making the process more humane and bearable for all involved. Then line your knife between the eyes and quickly and forcefully chop the lobsters right down the center from head to tail. The hard part is officially over. Preheat the grill.
Mix 6 tablespoons butter with 2 minced garlic cloves. Slather the insides of the lobsters with half the garlic butter, and liberally salt and pepper. Then place the lobsters on a hot grill, shell side down. Grill for 5 minutes, or until the meat is white and opaque. Do not over cook!
Meanwhile, set a large pot of salted water over high heat to boil. Cook the pasta according to package instructions. In a separate large skillet, saute the shallots, garlic, parsley and fennel with 2 tablespoons remaining butter and 1 tablespoons olive oil, until soft and tender. Add the cognac, clam juice, tomatoes, tomato paste, and crushed red pepper until thick and bubbly. Salt and pepper to taste.
Use a small hammer or meat mallet to crack the lobster claws. Pick the lobster meat out of one whole lobster, leaving the other 2 halves intact. Roughly chop the lobster meat. Add the lobster juices and meat to the sauce and toss in the al dente pasta. Add the cream and toss and cook another 2 minutes. Place the remaining lobster halves on serving plates. Then slather them with more garlic butter. Finally pile the pasta high on top of the two plated lobsters and sprinkle with Parmesan cheese.