Preheat the oven to 350 degrees. Butter either a 9x11 baking dish or four cocottes.
Boil the pasta according to the directions on the box for al dente pasta. Drain it well.
Meanwhile, in a Dutch oven, on medium heat, melt the butter and cook the shallots until they're tender, for about five minutes.
Add the flour to the shallots and cook for two minutes. Then add the chicken stock and the heavy cream and cook for two more minutes. Add the salt and pepper and remove from the heat.
Stir a half cup of the sauce into a bowl with the beaten eggs. This is to temper, or heat up the eggs, so that they don't scramble in the hot sauce. Mix it with a spoon, and then add the warmed up eggs to the warm pot. Stir in the pasta, lobster, and the cheeses, and pour it into either one 9x11 pan or four small cocottes.
In a small skillet, melt the rest of the butter, on low heat. Make breadcrumbs out of the bread in the food processor. Cook them in the butter for three minutes. Stir in the herbs.
Scatter the bread crumbs over the pasta and cheese and bake for thirty minutes.