Preheat broiler to High; line baking sheet with parchment paper or Silpat.
In a medium bowl, combine all ingredients for the coleslaw; chill in the refrigerator.
Saute turkey and onion in oil in a nonstick skillet over medium heat for about 5 minutes. Drain and return to heat. Stir in ketchup, corn, beans, green chilies, brown sugar, mustard, cumin, salt; heat through 2-3 minutes.
Spoon turkey mixture into each of the four bottom buns and arrange on the prepared baking sheet. Top with 1/4 cup cheese. Broil top buns cut side up, along with the bottom buns until buns are toasted and cheese is melted, about 1-2 minutes (keep an eye on them, so they don’t burn!)
To serve, spoon slaw onto each sandwich and serve with a toasted top bun.