In a small bowl, whisk together the soy sauce, grated ginger, one teaspoon of honey, and one teaspoon of sesame oil.
Place the chicken breast in a shallow dish or bag, pour half of the marinade over it, and let it sit for at least 15 minutes.
While the chicken marinates, prepare the dressing by whisking the remaining sesame oil, honey, and rice vinegar in a large bowl.
Add the cabbage mix, shredded carrots, and thawed edamame to the dressing bowl and toss thoroughly to coat.
Heat a grill or skillet over medium-high heat and cook the chicken for 6-7 minutes per side until the internal temperature reaches 165°F.
Let the chicken rest for 3 minutes, then slice it into strips.
Serve the warm grilled chicken over the chilled, crunchy slaw.