In a large skillet, heat 3 tablespoons oil over medium heat until it flows easily and coats the bottom of the pan. Working in batches if necessary, add bread and cook, swirling and moving the bread around for even toasting, until browned, about 3 minutes. Flip bread slices, add remaining oil, and continue to cook until browned on both sides, about 3 minutes longer. If working in batches, or if the pan dries out too much, add more oil as needed. Transfer toasted bread slices to a work surface. Wipe out skillet. Top with mozzarella, pesto, artichokes, and mortadella. Close sandwiches. Transfer sandwiches to skillet and cook in a preheated 350°F oven until cheese is melted, about 5 minutes. Alternatively, transfer sandwiches to a toaster oven and bake at 350°F until cheese is melted. Serve right away.