Coat a stove-top grill pan or griddle with cooking spray and set over medium-high heat to preheat. Season both sides of chicken with salt and black pepper. Place chicken on hot pan and cook 3 to 5 minutes per side, until cooked through.
In a small bowl, whisk together rice wine, vegetable oil, wasabi paste, hot mustard, and ginger. Set aside.
Heat sesame oil in a large skillet over medium-high heat. Add slaw mix and soy sauce and cook 2 to 3 minutes, until wilted.
Arrange wonton wrappers on a flat surface. Top each wrapper with 1 heaping teaspoon of slaw mixture. Pull up sides and pinch the middle together, making a purse. Heat peanut oil in a large skillet over medium-high heat. Add purses and cook 1 minute, until bottom is golden brown. Add broth and bring to a simmer. Cover and steam 3 to 5 minutes, until purses are tender and translucent.
Serve 4 of the chicken breast halves with all of the vinaigrette spooned over top and all of the beggar's purses on the side. Reserve remaining chicken for stroganoff, if desired.
Recipe courtesy of Robin Miller, 2007