Boil water in a small pot. Once water has boiled, put in eggs and set a timer for 8 minutes. After 8 minutes, drain hot water and run eggs under cold water. Once eggs are cool, peel and cut into quarters.
Season chicken with salt and pepper. You can also use garlic salt if you prefer. Heat up a few tablespoons of oil into frying pan. Once oil is hot, add in seasoned chicken and cook for 8-10 minutes each side or until internal temperature of chicken is 165ºF. Remove chicken from heat and let chicken rest for a few minutes. Cut chicken into slices or bite-sized pieces.
While chicken is cooking, prepare following next steps. Clean and cut lettuce, cucumbers, and red onions to preference. In a bowl, mix all salad dressing ingredients (ponzu, rice vinegar, soy sauce, sesame oil, brown sugar, and sesame seeds). Set aside.
To make crispy wonton strips, cut wonton strips into strips. Separate the wonton strips from each other. Using medium heat, heat up oil in a pan and fry wonton strips in batches. Fry wonton strips until golden. Cool fried wonton strips on paper towels. Set aside. You can also use store bought wonton strips if you don't want to deal with this additional step! Grocery stores will usually sell them in the salad aisle next to the croutons. Store bought crunchy chow mein noodles would also be delicious in this salad!
To assemble salad, put lettuce, cucumbers, onions, and eggs into a large bowl. Top salad with chicken and fried wonton strips. Generously drizzle ponzu soy dressing over salad and mix before serving.