Using hand cheese slicer, slice cheese about 1/8 inch thick; cutting slices in half so slices are square. Set aside.
Butter bread on both sides. Set aside.
On a griddle over medium heat, melt a teaspoon of butter and add lobster to warm, about 2 to 3 minutes or until warm. Remove lobster to plate.
Place buttered cheese bread slices on griddle to warm. Remove to plate.
Assemble ingredients back on griddle in this order: cheese bread slice, slice of cheese, lobster, cheese slice, basil pesto spread evenly over cheese, slice of cheese bread. Brown the sandwich until cheese melts.
Remove to plate; slice and serve with pickles.
Makes 2 servings.