For the slaw: Toss the cabbage with the lime juice, sriracha, salt and pepper in a large bowl. Cover and chill until ready to serve.
Cut the mangos into spears. Reserve 12 spears for your burgers. Chop the remaining spears for your slaw. Add them to the slaw just before serving along with the scallions and mint and toss to finish.
For the burgers: Combine the ground beef, teriyaki sauce, sriracha, ginger, garlic, salt and pepper in a medium bowl. Mix with your hands until combined. Form into 6 patties roughly 3/4-inch thick and 4 inches in diameter.
Brush a grill, grill pan or skillet with vegetable oil and heat on medium-high. When nice and hot, add the patties and cook for about 4 minutes per side for medium-rare. Take them off the heat.
To build the burgers: Spread mayonnaise on the bottom bun. Season with salt and pepper. Place a lettuce leaf on top of the seasoned mayo and top it with a patty, 2 slices of avocado, 2 spears of the reserved mango and the bun lid. Repeat with the 5 other burgers. Serve the slaw on the side.