Place chicken breasts in a large ziplock bag with the green onions then season with salt and pepper and set aside. Combine Tamari, brown sugar, sesame oil, sesame seeds, chili sauce, ground ginger, smashed garlic, and lime juice in a bowl then whisk to combine. Reserve 1/3 cup marinade then pour the remaining marinade into the bag with the chicken and green onions. Refrigerate for at least 30 minutes and up to 5 hours.
Preheat grill over high heat for 10 minutes (I like to let my grill get to at least 400 degrees.) Turn heat down to medium then spray chicken very well with nonstick spray and place sprayed side down on the grill. Grill for 3-4 minutes a side with the lid closed, spraying the top sides before flipping. Remove chicken to a plate then let rest for 10 minutes.
For the Snap Pea Slaw:
Add ingredients to a large bowl with the reserved marinade then toss with tongs to combine. Taste then add extra lime juice, salt, and pepper if necessary. Top chicken with slaw then serve.