3 cups finely shredded Napa cabbage
½ cup thinly sliced green onions, divided
3 tablespoons seasoned rice vinegar
4 teaspoons minced garlic
4 teaspoons fresh ginger, divided
1 tablespoon toasted sesame oil, divided
1½ teaspoons Asian chili garlic sauce, divided
¼ cup mayonnaise
1½ pounds ground beef
2 tablespoons soy sauce
4 hamburger buns, split
Heat grill to high - 450 to 550 degrees.
Mix cabbage, ¼ cup green onions, the vinegar, 1 teaspoon each garlic and ginger, 2 teaspoons sesame oil, and ½ teaspoon chili sauce in a large bowl. Set relish aside, stirring occasionally. In another bowl, mix mayonnaise with remaining 1 teaspoon chili sauce.
Combine beef, soy sauce, and remaining ¼ cup green onions, 1 tablespoon each garlic and ginger, and 1 teaspoon sesame oil. Shape into 4 patties, each about ½-inch thick.
Oil cooking grate. Grill burgers, covered, turning once - 7 to 8 minutes total for medium. In the final minutes, toast buns.
Spread bun bottoms with chili mayonnaise. Set burgers on buns. With a slotted spoon, put some cabbage relish on each. Serve with remaining relish.