Warm 2 tablespoons olive oil on a grill pan over high heat. Season steaks with salt, pepper, and 1 tablespoon soy sauce. Grill steaks 5 to 6 minutes on each side (they will be medium rare). Let steaks rest 10 minutes before slicing.
Drizzle asparagus with 2 tablespoons olive oil and remaining soy sauce. Place on the grill pan for 3 to 4 minutes until soft and lightly charred.
Toss arugula and grilled asparagus together, sprinkle with scallions, walnuts, and sesame seeds. Lay steak slices on top.
Whisk together all vinaigrette ingredients and lightly drizzle over salad. Garnish with lime zest and extra sesame seeds.