Preheat broiler.

With a sharp knife on a solid surface, put the knife through the head of the lobsters to kill them instantly and then flip them over and split lengthwise down the middle, keeping the back of the shell intact. Remove the roe and tomalley and discard. Pull the claws off and remove the tail meat from the shell and set aside.

Place the bodies on a baking sheet and broil the bodies until bright red, about 3 to 5 minutes, and set aside.

In a pot of boiling salted water, cook the lobster claws for 5 minutes and cool to room temperature until ready to serve.

In a large skillet over medium heat add the olive oil and lobster tail meat; cook until meat turns white, about 2 minutes. Add crabmeat and stir to combine. Add the shallots and garlic and cook for 1minute while shaking the pan to prevent burning. Remove the pan from the heat and add the brandy (the alcohol will ignite, so be careful) and return the pan to medium heat. Add the heavy cream and Dijon mustard and cook until reduced by half. Add the Parmesan and fold it in to melt. Add the chopped tarragon and season with salt and pepper. Stuff the mixture in the lobster shells and sprinkle the top with the bread crumbs. Broil until browned, about 4 to 5 minutes. Reheat the claws for just a1minute and serve together.