Prepare the Bread: Take two slices of sourdough and spread basil pesto evenly on one side of each slice. This will be the inside of your sandwich.
Assemble the Sandwich: Place sliced mozzarella on top of the pesto on one slice. Add the chopped sun-dried tomatoes on top of the cheese, and sprinkle with salt and pepper. Top with the second slice of bread, pesto side down.
Butter the Outside: Spread a thin layer of softened butter on the outer sides of the sandwich. This will help create a golden crust.
Grill the Sandwich: In a non-stick skillet over medium heat, place the sandwich and grill for about 3-4 minutes on each side, or until golden brown and the cheese has melted. Press down gently with a spatula for even grilling.
Serve and Garnish: Once grilled, remove the sandwich from the skillet and let it cool for a minute. Cut it diagonally, and if desired, garnish with fresh arugula on the side.
Enjoy: Serve warm, and savor the combination of gooey cheese with the fresh flavors of pesto and sun-dried tomatoes!