Cook corn: Either husk ears and grill until browned all over, or microwave in the husk 2 minutes.
Meanwhile, make dressing: Whisk miso, lemon juice, mustard, and shallot in a small bowl. Whisking constantly, drizzle in oil. Season dressing with salt and pepper.
Put green onions in a small bowl and cover with cold water. Set aside 10 minutes to crisp and curl. Meanwhile, slice kernels from cob into a serving bowl.
Drain green onions and add all but about 2 tbsp. to corn, along with chicken. Pour in dressing, toss to coat, and season with salt and pepper. Add avocado chunks and fold in gently to combine. Top with remaining green onion. Serve immediately.
*Find mild shiro miso, a widely available Japanese seasoning paste of fermented soybeans and rice, in the refrigerated section by the produce.