Heat a large skillet on the stove over medium heat.
Butter one side of each slice of bread, and on the opposite side of one slice spread the pesto, mozzarella, and goat cheese. Add sliced tomato and arugula on top of the cheeses. Top with the other piece of buttered bread, with the butter side facing up.
In skillet, cook sandwich 4-5 minutes per side until cheese is melted, and the sandwich looks crispy.