Make Arugula Basil Pesto. Add arugula, basil, Parmesan, walnuts, lemon juice, olive oil, water, garlic, salt and pepper to a food processor bowl, and process until smooth. Taste and add more salt, pepper or lemon juice, if necessary.
Preheat grill to medium high.
Form ground beef into twelve slider patties and grill until cooked to desired doneness.
Spread bottom half of each roll with Arugula Basil Pesto. Layer on tomato slices, slider patty, Mozzarella and desired amount of basil leaves and balsamic drizzle. Top with roll lids.