Boil the lobsters for 6 minutes. Cool on an ice bath. Split the lobster in half. Saute the garlic in 1 tablespoon of the butter. Add the anchovies and the rest of the butter and puree the mixture in a blender.
Rub the cut side of the lobster with the anchovy butter and grill for 2 minutes on each side.
Recipe courtesy of Chef Lisa Somma, Soho Restaurant, Long Branch, NJ