Cook pasta al dente according to package directions, transfer to a colander, and drain.
Bring a large pot of water to a boil over high heat. Fit a metal mixing bowl over it to create a double boiler. Add all cheeses (except Parmesan) and 1-½ cups of the heavy cream.
Melt cheeses, stirring often to prevent burning. If mixture seems too stringy or clumpy, add some of the remaining cream. The texture should be velvety and a bit loose--the consistency of cheese soup.
Preheat oven to 350 degrees F. In a sauté pan over medium heat, melt butter. Add chives, shallots, salt, and pepper. Cook, stirring, for 3 to 4 minutes, or until shallots are tender. Add lobster and cook, stirring, for 1 to 2 minutes.
In a large bowl, combine lobster mixture and pasta and stir. Slowly add as much cheese mixture as desired.
Transfer mixture to an oven-safe dish and top with Parmesan and bread crumbs. Bake for 12 minutes, or until browned on top and warm in the middle.
