In cup, stir mayonnaise and soy sauce until blended; set aside. From limes, grate 1/2 teaspoon peel and squeeze 3 tablespoons juice. In large bowl, toss together lime peel and juice with cabbage and1/4 teaspoon salt; set aside.
Lightly spray ridged grill pan or skillet with nonstick cooking spray, then heat on medium until hot.
Meanwhile, in medium bowl, combine beef, cilantro, green onions, ginger, sesame oil, crushed red pepper, and 1/4 teaspoon salt until blended, but do not overmix. Shape beef mixture into four 3/4-inch-thick burgers, handling meat as little as possible for best texture.
Place burgers in hot grill pan; cook 10 to 12 minutes for medium or until desired doneness, turning burgers over once halfway through cooking.
Serve burgers on buns with slaw and soy mayonnaise. Serve with any additional slaw on the side.
