Combine the chicken, green onion, soy sauce, garlic powder, sesame oil, carrots, ginger, bread crumbs and egg, gently mixing to incorporate. Divide the mixture into 4 patties and set aside. Add olive oil to a cast iron pan and heat to medium-high heat. Place the patties in the pan, turning once until done, 6 to 8 minutes per side or until the internal temperature is 160 degrees F.