Place sliced mozzarella in a single layer between several paper towels. Place a cutting board on top of the covered mozzarella and add 2 pounds of weight for 15 minutes, unopened soup cans work well. Doing this will remove the excess moisture and will prevent your Panini from becoming soggy while in the press.
Preheat the panini press to medium-high heat.
To make the pesto. Add to the bowl of a food processor, the basil, garlic, pine nuts, and parmesan. Pulse while slowly adding ½ cup olive oil until smooth and desired consistency. Add the salt and pepper and pulse a few more times to incorporate.
Using a sharp bread knife, slice your focaccia loaf down the middle vertically and then down the middle horizontally, creating 4 servings. Slice each section in half to create a top and bottom of your sandwich and lightly brush the outside of each piece with olive oil. Oiled side down, liberally spread the pesto on the inside of each half. On the bottom half, add the sliced mozzarella, tomato, and arugula. Place the tops of the bread on each sandwich and place in the panini press.*
Cook 5 minutes, or until the cheese has melted and the bread is golden brown. Transfer the panini to a cutting board and cut in half. Serve immediately.
Notes
*Tip - If you do not have a Panini press, you can heat a heavy skillet over medium-high heat and cook each side for several minutes, using a lid or another skillet to press the sandwich while cooking.