How to Make It
Fill a large stockpot with 2 inches of water, add 2 tablespoons of the salt and bring to a boil over high heat. Put the lobster in the boiling water, head first, and cook until it turns red, about 12 minutes. With tongs, transfer the lobster to a bowl to cool.
Remove the meat from the lobster knuckles and claws. Twist the tail off the body; reserve the greenish tomalley and red roe. Split the tail lengthwise and remove the tail meat. Pull out and discard the black intestinal vein. Cut all the lobster meat and the roe into 1/2-inch dice and place in a bowl. Add the tomalley.
In a small saucepan, melt 4 tablespoons of the butter over moderately low heat. Add the red pepper, celery and 1/4 cup of the carrots and cook, stirring, until the vegetables are almost tender, about 5 minutes. Let cool to room temperature.
In a food processor, combine the shrimp and egg white and puree until very smooth. Scrape the puree into a bowl and fold in all the lobster meat, cooked vegetables, bread crumbs, chives, the remaining 1/2 teaspoon of salt, the black pepper and a pinch of cayenne. Cover and refrigerate until chilled.
Remove 10 large intact outer leaves from the head of cabbage and set aside. Cut the remaining cabbage in half; core and shred it.
In a large saucepan of boiling salted water, blanch the whole cabbage leaves 2 or 3 at a time, just until tender, about 3 minutes. Drain the leaves and let cook. Add the shredded cabbage to the boiling water and cook for 1 minute. Drain the cabbage in a colander and refresh under cold running water; drain again.
In a large skillet, melt 1 tablespoon of the butter. Add the onion and sauté over moderately high heat until browned, about 4 minutes. Add the shredded cabbage and cook for 2 minutes. Season with salt and pepper and let cool completely.
Preheat the oven to 350°. Butter an 11-by-9-inch glass baking dish. Select the 8 best-looking cabbage leaves and pare down the thick central ribs so that they are flush with the leaves. Spread the leaves on a work surface and form one-eight of the lobster filling into a 3-inch log across the center of each leaf. Top with one-eighth of the shredded cabbage mixture. Fold the 2 sides of each cabbage leaf in toward the center, then snugly roll up the leaf; use the 2 extra cabbage leaves to patch up any tears. Arrange the cabbage rolls, seam side down, in the prepared baking dish, leaving a little bit of space between the rolls.
In a large skillet, melt 1 tablespoon of the butter over moderate heat. Add the mushrooms, shallots and the remaining 1/2 cup of diced carrots. Cook, stirring, until the vegetables begin to brown, about 6 minutes. Add the stock and bring to a simmer. Season with salt and pepper and pour over the cabbage rolls. Cover the dish with foil and bake for about 25 minutes, or until the rolls are firm and heated through.
Transfer the cabbage rolls to a warmed platter and cover loosely with foil. Pour the juices from the baking dish into a small saucepan and bring to a boil. Off the heat, whisk in the remaining 2 tablespoons of butter, 1 tablespoon at a time. Add the chopped herbs, season with salt and pepper and pour over the cabbage rolls. Serve at once.