Prepare the sauces first so they're ready to use when needed. In a small bowl stir together the ingredients for the stir fry sauce (soy sauce, sesame oil, and brown sugar). In a separate small bowl stir together the sriracha and mayonnaise.
Mince 2 cloves of garlic, grate about one teaspoon of fresh ginger, and slice three green onions.
Without opening the package of ramen, use a rolling pin or mallet to crush the noodles into small pieces. Once crushed, open the package and discard the seasoning packet.
Chop the chicken into small 1/2-inch pieces.
Place a large skillet over medium-high heat. Once hot, add the cooking oil and swirl to coat the surface of the skillet. Add the chicken pieces and sauté until they're cooked through (3-5 minutes). Add the garlic and ginger to the skillet about half way through cooking the chicken.
Once the chicken is cooked through, add the coleslaw mix (shredded cabbage and carrots). Continue to sauté for about 2 minutes more, or just until the cabbage begins to soften slightly (do not overcook at this step).
Add the stir fry sauce to the skillet and continue to sauté for 1-2 minutes more, or until the cabbage has softened to your liking (I prefer mine still slightly firm).
Finally, turn off the heat, stir in the crushed ramen, and top with sliced green onions and a drizzle of sriracha mayo.