The the vegetable oil over medium high heat in a large sauté pan.
Place each chicken breast into a large plastic zip top bag, one at a time, and pound the chicken with a mallet until it's about 1/2 inch thick throughout.
Prepare a breading station, one bowl of flour, one bowl of whisked eggs (season with salt and pepper) and one bowl of bread crumbs.
Dip each chicken breast into the flour mixture. Followed by the egg mixture. Then dip into bread crumbs.
Carefully place the chicken in hot oil over medium high heat and cook for about 2 minutes until the bread crumbs are golden brown. Using a pair of tongs, flip the chicken over and let it continue to cook on the opposite side. Once the chicken is fully cooked, remove it from the pan and set it on a paper towel lined plate to rest. Repeat this process with the remaining chicken.
Once all the chicken is cooked, slice the ciabatta loaves in half. Slather the bottom layer of the bread with marinara sauce and place a chicken breast on top. Add another spoonful of sauce, a few slices of fresh mozzarella, some freshly grated parmesan cheese and then top it with some basil. Add the top of the bread on and carefully place the panini in a heated panini press. Close the panini press and cook for 4-5 minutes until the bread has grill marks and it's slight toasted.
Repeat this process with the remaining paninis.
These can be serve immediately, or if you're taking them on a picnic, wrap them with aluminum foil and pack away.