To spatchcock the quail, cut each bird down the back. Place the birds breast side up and press down with the palm of your hand to flatten them. Transfer the quail to a bowl or zip-top bag.
In a small mixing bowl, combine the huli-huli sauce ingredients and stir until dissolved. Reserve ¼ cup of the sauce for basting and dipping. Pour the remaining sauce over the quail and refrigerate overnight.
When you are ready to cook, prepare a grill to 350–400°F for direct-heat cooking. Remove the quail from the sauce, allowing the excess to drip off, and place them on a cookie sheet. Lightly season the birds with salt and brush with oil.
When the grill is hot, place the birds breast side down and cook until well marked—keep a close eye on them, as the sugar in the sauce can burn easily. Flip the birds, baste with the reserved sauce, and continue cooking until done. You're aiming for an internal temperature of 150°F in the breast area.
Serve the quail immediately with hot white rice and the reserved sauce for dipping. Garnish with chopped green onion.