Preheat a panini style grill. Lightly grease with nonstick spray.
Heat a sauté pan over medium heat.
Coat the eggplant slices in the egg then coat well with the breadcrumbs. Once the pan is hot add the oil and fry on both sides until golden brown and soft. Place on a paper towel-lined plate to drain any excess oil, season with salt and pepper, then set aside.
Mix the mayo, basil, and garlic together and spread on the wrap. Layer with mozzarella, spinach, eggplant, ham, and tomatoes seasoned with salt and pepper. Fold in the ends of the wrap and roll up tightly.
Place the wrap onto the panini grill and cook until golden brown and the cheese is melted.Alternatively, lightly grease a nonstick pan on medium heat, place the wrap seam side down cook to golden brown then flip over and do the same to the other side.