Preheat a grill to medium high. Bring a large saucepan of water to a boil. Turn off the heat, add the rice noodles and stir to loosen. Let sit until tender, 2 to 4 minutes; drain and rinse thoroughly under cold water. Shake out as much water as possible and transfer the noodles to a medium bowl. Toss with 1 teaspoon sesame oil and season with salt and pepper.
Combine 1/4 cup water, the chili sauce, fish sauce, lime juice and 2 pinches salt in a small bowl. Set aside.
Season the steak on both sides with salt and pepper and rub all over with the oyster sauce and remaining 1 teaspoon sesame oil. Grill the steak, 5 to 6 minutes per side for medium rare. Transfer to a cutting board and let rest 10 minutes.
Meanwhile, pull off 16 outer leaves from the cabbage head and cut off the leafy tops. Thinly slice the steak against the grain. Fill the cabbage leaves with the noodles, mango, steak, peanuts, cilantro and basil. Season with salt. Serve with the sauce.