Marinate the chicken - a simple marinade of lime juice, oil, ginger, pepper and garlic. Just toss in a baggie and add the chicken and mix till well coated. Just let set in the refrigerator all day, or even 3-4 hours.
The sauce - this can be made ahead and all ready for you. In a large bowl, just basically mix everything. If making ahead NOTE, I would hold off adding the cilantro until the end so it has a fresh taste. Otherwise, combine all the other ingredients. The lime wedges are a garnish on each persons plate, so you don't have to worry about those. You will need to add the cilantro 15-20 minutes to the dressing before you add it to the pasta just to combine the flavors. But do that as the pasta is cooking.
Grilling - Grill the chicken, outside, inside grill pan or saute pan. Either works. I prefer the outdoor grill, but they all work. There should be enough oil on the chicken so you shouldn't have to add any when cooking. Just cook until done and still moist. Depending on the size 4-6 minutes per size, thicker cuts will take longer but don't over cook. Remove from heat, cover with foil and let rest.
Make the salad - A quick chop of a red pepper and I like thin strips, but chopped or diced in fine, carrots cut in match sticks 1” long. NOTE (you can by shredded or thin sliced carrots already in the vegetable aisle and that is just fine. Two (2) carrots is about 1 cup may be a bit more. Not important as to how much. Feel free to use as many of your favorite vegetables as you like. Scallions, (white and green cut in 1 angle pieces). I also like extra scallions in my dishes. One (1) small seedless cucumber cut lengthwise and then thin sliced. Radishes and off course the mushrooms - shitaki, just thin sliced. Toss all and wait for the pasta.
Finish - the dish with the pasta. I just cook the pasta according to directions, drain and cool a minute or two. I do not mind eating this dish warm or cold. It is equally as good both ways. I have tossed the pasta warm with the sauce, added the chicken and served. Or I have made it and let chill before serving. Either or - it is a great salad! Top with a fresh lime wedge and squeeze to give it great flavor.