In a large bowl, combine the soy sauce, brown sugar, ginger slices, garlic, sesame oil, juice of 1 lime, and red pepper flakes. Stir to combine.
Cut the steak into 1-1.5" chunks. Add to the marinade and toss to coat. Marinade for at least one hour.
While the steak is marinating, make the slaw. In a large bowl, combine all of the ingredients except the cabbage and whisk together. Season to taste with salt and sriracha.
Slice the cabbage thinly to a shredded consistency. Add to the slaw sauce and toss to coat. Refrigerate until ready to serve.
When the steak is done marinating, thread the pieces onto skewers (do not use the ginger slices). I fit approximately 1/2 pound on each skewer, 4 skewers.
Grill over medium heat until you reach your desired doneness. The time this takes will depend on the size of the steak pieces as well as the exact temperature of your grill. For medium, this took us approximately 3 minutes per side. Serve immediately with the slaw. Garnish with sesame seeds and sliced green onion if desired.