Combine the chicken, celery, carrot, garlic, finely diced scallion, blue cheese, panko, egg and 1/3 cup of the wing sauce in a large bowl. Season with salt and pepper. Using your hands, lightly mix everything together, taking care not to overmix.
Using a light touch, form the mixture into balls, each about 1 inch in diameter.
Heat oil in a large Dutch oven over medium heat. Working in batches, put the meatballs in the Dutch oven in a single layer (don't crowd the pan) and cook until lightly seared and just browned, about 2 minutes per side. (The meatballs will not be cooked through at this point, they will finish cooking in the sauce.) Transfer meatballs to a plate as they cook.
Wipe out the Dutch oven, then return the meatballs to the pot. Add the remainder of the bottle of wing sauce (about 9 ounces) to the pot. Simmer over low heat, covered, until the meatballs are cooked through, about 30 to 60 minutes.
Spoon the meatballs into a serving dish, top with warm sauce and garnish with blue cheese and the sliced scallions. Serve immediately.
The seared meatballs can also be transferred to a slow cooker and cooked on the high setting until cooked through, about 2 hours.