In a shallow dish, combine the plain bread crumbs with the panko bread crumbs until well incorporated. Pour the flour in a separate shallow dish, and whisk the eggs with a splash of water in a third shallow dish. Season the flour and eggs with a bit of salt and pepper.
Cut the mozzarella into twelve even, 2 by 2 squares. To dredge the mozzarella coat the squares of cheese into the flour mixture, then into the egg mixture, then into the bread crumb mixture, then back into the egg and once more into the bread crumbs. Place the coated mozzarella pieces on a baking sheet lined with parchment paper. Chill the mozzarella pieces in the freezer for at least 1 hour. It's best to freeze them slightly before frying so that they don't melt too fast in the hot oil.
Fill a cast iron skillet with about 1/4-inch of oil and set over medium heat. Check the temperature with a deep-fry thermometer, once it reaches 360 degrees, carefully drop in a few pieces of the chilled mozzarella and fry until golden brown and crispy on the outside, about 1 to 2 minutes. Flip over and continue to cook for about minute. Drain with a slotted spoon and transfer to a wire rack set over a baking sheet. Continue to fry the remaining mozzarella pieces. You can keep them warm in a preheated 250 degree F oven until ready to assemble.
To assemble the sliders, split the rolls in half. Lay a handful of arugula on the bottom half of each bun, top with a slice of tomato, a fried mozzarella square, a spoonful of marinara, and a little bit of basil. Replace the top lid on and skewer with a long toothpick to hold in place. Serve immediately while the cheese is still warm. Enjoy!