Spread bread pieces on a work surface. Spread 1/2 tablespoon olive tapenade on half the pieces, then cover with a slice of mozzarella, then cover with the remaining bread slices. Butter both sides of the sandwich and grill in batches in a panini press until browned on both sides. Put on a platter and cover with foil to keep warm until serving.
Put anchovies, garlic and thyme in a blender or food processor and puree. Add olives and olive oil, and pulse to a smooth paste. If it is too thin, add more pitted olives. If it is too thick, add more olive oil.