1) Preheat a grill.
2) 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.
3) Remove the roe and tomalley and discard. Pull the claws off and remove the tail meat from the shell and set aside.
4) Place the bodies on a baking tray and grill until bright red, about 3-5 minutes, and set aside.
5) In a pot of boiling salted water, cook the lobster claws for 5 minutes and cool to room temperature until ready to serve.
6) 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 1 minute 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 double 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.
7) Stuff the mixture in the lobster shells and sprinkle the top with the breadcrumbs. Grill until browned, about 4-5 minutes. Reheat the claws for just a minute and serve together.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe in the proportions indicated and, therefore, we cannot make any representation as to the results.