To make the marinade: Whisk together ginger, garlic, soy sauce, sugar, lime juice, fish sauce, black pepper, olive oil, and toasted sesame oil in a bowl. Transfer it to an airtight container with a lid or pour it into a resealable plastic bag. Place the steak in the marinade, seal, and let it marinate for at least 6 hours or up to 12 hours.
When you are ready to cook the meat, remove it from the marinade onto a large plate lined with paper towels and pat dry to remove the excess liquid. Season lightly with ¼ teaspoon kosher salt.
To cook the steak: Preheat a gas grill* to 450 degrees. Grill, turning a few times until lightly charred on both sides and a thermometer inserted in the thickest part of the steak registers 120 degrees F for medium-rare or 130 degrees F for medium. This takes about 9-11 minutes in total. Cover it with aluminum foil, and let it rest on a cutting board for 10 minutes. Cut it into 1-inch pieces right before serving the salad.
To make the salad dressing: Whisk together lime juice, hot chili paste, avocado oil, garlic, fish sauce, sugar, and honey in a bowl. Give it a taste and add more salt if needed. Set it aside.
To cook the noodles: Cook noodles in a small pot of boiling water for 3 minutes. Drain and transfer to a large bowl. Drizzle with sesame oil and give it a toss.
To assemble the salad: Place the mango, arugula, shredded carrots, scallions, cabbage, and tomatoes in the bowl with the noodles. Drizzle it with the prepared dressing. Give it a gentle toss to combine.
Add sliced steak, avocado, fresh cilantro, basil, mint, and peanuts. Gently toss to combine.
Divide amongst four plates and serve with wedges of lime on the side.