Don't feel hemmed in by the ingredients list here: If you'd prefer to cut up a rotisserie chicken or a package of 5-spice tofu instead of marinating and grilling the chicken breasts, please do. Likewise, use whatever greens you like (lettuce, say, or spinach) and any other veggies that appeal to you (I would have added sugar snap peas, carrots, jicima, and cilantro, if we'd had them, and I would have added scallions, if my kids wouldn't have spent all of dinner picking them out). And, finally, if you can't bring yourself to deal with the noodles — which I totally understand, since it is the only part of this recipe that is actually kind of a pain -- skip them and add more peanuts. It will still be delicious.
Miso is a Japanese fermented-grain seasoning that's like a cross between soy sauce and library paste and a chorus of angels singing about salt. If what you already have in your life is red miso, try using that, but use less at first since it's even saltier. In a pinch, bottled Annie's Shiitake and Sesame Dressing is a fine way to go, for both the marinade and salad.
Make the dressing by whisking together the miso, vinegar, ginger, sugar, and soy sauce until well blended, then whisk in the oil and, finally, whisk in the water. Taste the dressing on a piece of cabbage or cucumber. Does it seem balanced and good? Add a little of this or that (tamari, oil, vinegar, or sugar) if it needs it.
Meanwhile, quarter the cabbage lengthwise, cut out and throw away the hard core, then slice the cabbage leaves thinly. Spread it out over a large plate or a very wide salad bowl.
Peel the cucumber, cut it in half lengthwise, then scoop out the seeds using a teaspoon or a melon baller. Slice the cucumber and arrange it, along with the sliced celery, over the plate of cabbage.
Grill or broil the chicken breasts until the juices run clear, about 4-5 minutes per side. Let the chicken cool on a cutting board while you fry the noodles.
Heat about 1/2 inch of vegetable oil in a very small pan over fairly high heat. When it is just smoking, drop in a test noodle: it should puff up and turn from clearish to white immediately. Now add the whole little skein of noodles, let it puff up, then flip it over and cook the other side, moving it around in the oil to puff as much of it as you can. Drain it on paper towels or a paper grocery bag. Because you are cheating the oil here (I can't bear to heat 2 inches of oil to deep fry an ounce of noodles), you're going to end up with some noodles in the middle that don't puff up. You can either break off the puffed noodles and refry this core, or else just use what you can and toss out the middle few unpuffed noodles, which you don't want in you're salad because they're like eating fish bones.
Slice the chicken.
Dress the greens lightly before arranging the orange slices around them, then the chopped peanuts, then the chicken.
Drizzle the chicken with a little more dressing and, finally, top with the puffed noodles and serve.