Toss together kale, cilantro, green onions, and carrots. Whisk together lime juice, soy sauce, honey, and 1 tablespoon olive oil in a small bowl; pour over kale mixture, and toss to coat. Set aside while preparing chicken, tossing occasionally.
Break ramen noodles into pieces. Process ramen noodles, seasoning mixtures from ramen packages, ginger, and cayenne pepper in a food processor until combined, 1 minute. Transfer mixture to a shallow dish, and set aside.
Place each chicken cutlet between two sheets of heavy-duty plastic wrap, and flatten to 1/4-inch thickness, using a rolling pin or flat side of a meat mallet. Dip each cutlet in eggs, and dredge in ramen mixture, pressing to adhere.
Cook half of chicken in 2 1/2 tablespoons hot olive oil in a large skillet over medium until golden brown and done, 2 to 3 minutes on each side. Place on a wire rack in a rimmed baking sheet, and keep warm in a 200° oven. Repeat procedure with remaining chicken and olive oil.
Sprinkle peanuts over kale mixture, and serve with cutlets.