In a food processor, combine the nuts and garlic and pulse to a coarse crumb. Add the breadcrumbs, Parmesan, parsley, salt and a few turns of pepper and pulse to combine. Add the eggs and process until the mixture holds together in a ball. Roll 1 1/2 tablespoon-sized balls, packing just firmly enough so they hold together but not so much that they toughen. Put the balls on a plate or sheet of parchment paper.
Warm the tomato sauce in a large pot over medium heat.
Heat 1/4 inch of oil in a skillet over medium-high heat and cook the balls in batches, turning until they're golden brown on all sides, 7 to 10 minutes. (Alternatively, you can deep fry the suckers if that's what you're into.) Add the balls to the tomato sauce.
Put 1 slice of mozzarella, 2 balls and 1 basil leaf on the bottom of each roll. Top with the top of the slider bun and serve with additional marinara sauce and chopped parsley or basil on the side.