In a medium saucepan, sweat the onion, carrot and celery until soft, in 1 tsp. of the butter. Add the garlic, tarragon and tomato paste and shells and cook for several minutes, stirring regularly. If using shrimp shells, they should turn pink, since crab and lobster are already cooked, just break up the shells with a spoon or meat tenderizer if they are too thick. Add brandy to deglaze and cook until almost dry. Add the remaining butter. Cook over low heat for twenty minutes, stirring regularly. Strain through a fine meshed strainer into a bowl and place in the refrigerator. Once the butter has nearly set, spoon onto a sheet of plastic wrap and roll into a log, tying the ends tightly and return to the refrigerator.
Season the 6oz Filet Mignon on both sides with salt and pepper and grill to desired doneness, about 4 minutes per side for medium. Slice the butter into thick slices and place on top of the 6oz Filet Mignon while it is resting. The heat from the 6oz Filet Mignon should start melting to butter, if it doesn't place it under a broiler for around fifteen seconds.