Snap or cut off the woody ends of the asparagus and cut into 1-inch pieces.
In a medium saucepan, bring a ½-inch of water to a boil over high heat. Add asparagus and cook, uncovered, until crisp-tender, 3-5 minutes.
Meanwhile, peel and mince or grate ginger; transfer to a medium bowl.
Add soy sauce, oil, and vinegar to the bowl with the ginger; whisk to combine the dressing.
¼ cup soy sauce
3 tbsp toasted sesame oil
4 tsp rice vinegar
When the asparagus is done, drain and add to the bowl with the dressing; set aside.
Preheat a grill pan, outdoor grill, or regular skillet over medium-high heat.
While the grill pan heats up, pat the steak dry with paper towels and place on a plate; season with salt and pepper on both sides.
1 ½ lb striploin (New York strip) steak
½ tsp salt
¼ tsp black pepper
Once the grill pan is hot, coat with oil. Add steak and grill until desired doneness, 2-5 minutes per side. Transfer to a clean plate, cover loosely with aluminum foil, and set aside to rest for about 5 minutes.
2 tsp toasted sesame oil
Meanwhile, peel and trim carrots. Using a julienne (or regular) peeler, peel carrots into thin noodle-like sticks; add to bowl with the asparagus.
Shave cilantro leaves off the stems; discard stems and mince the leaves.
Slice lime into wedges.
Thinly slice steak against the grain and add to the bowl with the vegetables. Toss to combine.
Separate the lettuce into leaves. Pile leaves, in stacks of two per wrap, onto plates. Fill with steak, vegetables, and cilantro; sprinkle with sesame seeds. Serve with lime wedges on the side and enjoy!