Form the ground turkey or chicken into 2-ounce patties. Sprinkle both sides of each patty liberally with salt and pepper.
Heat a grill, grill pan, or cast-iron skillet over high heat, adding the canola oil if applicable. Cook the patties for approximately 3 minutes, then flip and continue cooking for an additional 3 minutes for medium, or continue cooking to your desired doneness.
Meanwhile, in a small saucepan over medium heat, bring the wing sauce and honey to a simmer. Remove from the heat and stir. Brush the wing glaze over both sides of the cooked patties.
Build the burgers by placing each cooked patty on the bun bottoms. Top with celery leaves and crumbled blue cheese. Smear the top buns with the Blue Cheese Dressing and place on top of the other ingredients. Serve immediately.
Using the tongs of a fork, mash together the blue cheese and mayonnaise in a small bowl. Stir in the buttermilk, sour cream, vinegar, sugar, garlic powder and onion powder. Season with salt and pepper. Cover and keep in the refrigerator until ready to use.