Preheat oven to 350˚. Butter a 9×9-inch baking dish.
Bring cottage cheese, mascarpone, sharp cheddar and milk to room temperature before processing. Place cottage cheese and mascarpone in a food processor; blend until smooth. Add milk, mustard, hot sauce, nutmeg, salt and pepper. Blend until fully mixed.
Add cheddar cheese and blend until fully combined. The mixture will be very thick.
Make broth: Bring 2 cups water to a boil with all broth ingredients except lobster. Add lobster. Cook 7 minutes, until lobster is pink and curled slightly. Remove lobster from pan; set aside to cool. Continue to boil the liquid until it is reduced to 3/4 cup. Drain lobster broth, keep hot, and set aside.
Remove lobster from shell, and cut into large chunks.
Place cheese mixture and lobster in a mixing bowl. Add enough lobster broth to thin the sauce to the consistency of pancake batter.
Boil 6 cups water; add pasta and salt. Cook for about 6 minutes. The pasta should be undercooked. Drain, and add to the cheese sauce. The hot pasta will melt the sauce. Stir well. Add more lobster broth if sauce is too thick.
Transfer shells and sauce to baking dish. Top with breadcrumbs. Cover and bake for 20–25 minutes until heated through.