Preheat the oven to 400 degrees F.
Bring a large stock pot with approximately 2 gallons of salted water to a boil over high heat. Add the lobsters and boil for about 8 minutes. Drain from water and shock in an ice bath. Once cooled, remove the knuckles, claws and tail from the body of the lobster by a slight twist and pull. Split the tail with a knife, remove the meat from the shell and set aside. Pull off the claw pincher. Crack the claws with a nutcracker and remove the meat. Set aside. Using kitchen shears cut through the knuckle portion and remove the meat. Give all of the lobster meat a good rinse and roughly dice. Put into a large bowl and set aside.
In the large bowl, add the mayonnaise, creme fraiche, shallots, lemon juice, chives, parsley, avocado, bacon, salt and pepper, to taste, and combine well. Cover and refrigerate before assembling the sandwich.
Toast the brioche rolls in the oven until slightly colored, about 4 minutes. Assemble the sandwich by putting a liberal amount of lobster salad on each roll and serve.