In a small bowl, mix mayonnaise, hoisin sauce and chili sauce. Refrigerate until serving.
In a large bowl, combine turkey, bread crumbs, green onions, 1 tablespoon soy sauce and ginger, mixing lightly but thoroughly. Shape mixture into twelve 1/2-in.-thick patties.
In a small bowl, whisk vinegar, sugar, oil and remaining soy sauce. Add carrots, onion, cilantro and sesame seeds; toss to combine.
Grill sliders, covered, on a greased rack over medium heat or broil 4 in. from heat until a thermometer reads 165°, about 3 minutes on each side. Spread cut sides of buns with mayonnaise mixture. Layer each bottom with a burger and 2 tablespoons slaw. Replace tops.