Prepare the chicken skewers: Cut chicken thighs in half lengthwise along the creases and halve the thicker portions to get 3 or 4 pieces each. Place chicken in a bowl. Pour in soy sauce, sake, mirin, brown sugar, green onions, ginger, and oil. Toss by hand until well combined and brown sugar is dissolved. Cover top in plastic wrap and marinate in the refrigerator for 2 to 6 hours.
Make the dressing: Combine mayonnaise, buttermilk, sour cream, and miso in a bowl. Add green onion, garlic, tarragon, dill, and chives. Season with black pepper and cayenne. Whisk dressing until thoroughly combined.
Thread chicken pieces onto skewers. Strain marinade into a saucepan and bring to a boil to make the glaze.
Preheat a grill for medium-high heat. Grill skewers, basting with some of the reserved marinade, until meat firms up and springs back to the touch, 4 to 5 minutes per side.
Serve skewers next to the miso ranch dressing and brush with reserved glaze.