Preheat oven to 450F.
Bring a large (oven safe) pot of water to a boil and season well with kosher salt (about 1 tablespoon).
Cook the pasta according to package directions, then drain and set aside.
Heat 2 tablespoons of butter over low heat in the same pot.
Gently dice the lobster into bite size pieces and add into the butter. Season with a pinch of salt.
Stir gently and cook for about 2-3 minutes or until the lobster. no longer translucent. Remove the lobster from the pot and set aside.
Next, add the heavy cream to the pot and bring to a simmer.
Add in the cheese, little by little, stirring as you go to make sure the cheese has melted well.
Now, add back in the lobster followed by the pasta. Toss well to make sure the pasta is well coated with the sauce.
Top with grated Parmesan cheese and breadcrumbs. Bake at 450F for about 10-15 minutes or until golden brown on top.