Preheat oven to 425°F. Finely chop white and light green parts of scallions and place in a large bowl; set aside. Thinly slice dark green parts of scallions and set aside. Add miso, maple syrup, ginger, soy sauce, garlic, and 4 tablespoons oil to chopped scallions in large bowl; whisk together until mostly smooth. Reserve ¼ cup miso mixture in a small bowl, and set aside.
Add chicken thighs to miso mixture in large bowl, and add ¼ teaspoon each salt and pepper; rub chicken thighs with mixture until evenly coated. Let stand, uncovered, at room temperature for 15 minutes.
Toss together squash, brussels sprouts, remaining 2 tablespoons oil, ½ teaspoon salt, and ¼ teaspoon pepper on a large rimmed baking sheet; spread in an even layer. Top with marinated chicken thighs. Bake the chicken until a thermometer inserted into thickest portion of thighs registers 165°F and vegetables are tender and browned, 40 to 45 minutes.
Meanwhile, whisk vinegar and toasted sesame oil into reserved ¼ cup miso mixture in small bowl until smooth and emulsified; set dressing aside.
Transfer chicken to a plate. Add arugula and reserved sliced scallions to baking sheet with vegetables; toss with reserved dressing until evenly coated. Return chicken to baking sheet; garnish with sesame seeds, and serve immediately.
