Make the dressing: whisk together white vinegar, canola oil, soy sauce, sesame oil, lime juice, brown sugar, ground ginger, salt, black pepper and minced garlic in a small bowl until sugar dissolves.
Marinate the chicken: pour half the dressing into a large zip-top bag, add the chicken cutlets (or pounded breasts), seal, and turn to coat. Refrigerate while you prepare the salad or up to a few hours.
Cook the orzo: bring a large pot of salted water to a boil, cook the orzo according to package directions until al dente, then drain completely and transfer to a large bowl.
Add the vegetables: to the warm orzo add chopped green onions, diced carrot, diced red pepper, chopped spinach and diced celery; toss to combine.
Dress the salad: pour the remaining half of the dressing over the orzo mixture and toss until everything is evenly coated. Chill in the refrigerator if not serving immediately.
Toast the almonds (if not already toasted): in a dry skillet over medium heat, cook slivered almonds until lightly golden and fragrant, stirring frequently; remove from heat and cool.
Grill the chicken: heat the grill to high, place marinated chicken on the hot grill, cover and cook about 3–5 minutes per side until cooked through (time varies by thickness). Remove and let rest briefly, then slice if needed.
Assemble and serve: transfer the orzo salad to a serving dish, sprinkle with toasted almonds and broken ramen noodles, arrange the grilled chicken on top and finish with a sprinkle of sesame seeds.