In a large bowl, gently combine turkey, bacon, BBQ sauce, liquid smoke and salt and pepper to taste.
Divide into 8 thin burgers. Put a mound of cheddar cheese in the middle of four patties then top with another patty and pinch edges together.
Heat 1 Tablespoon of olive oil in a grill pan over medium-high heat. Add burgers and cook for 4-5 minutes on each side or until cooked through.
Let burgers rest for a few minutes before serving. Place burger on a toasted bun and top with onion strings.
FOR ONION STRINGS: Use a sharp knife to thinly slice the onion. Place onion in a baking dish and cover with buttermilk. Set aside for 15 minutes (this helps mellow the strong onion taste). In the meantime, heat oil to 340 degrees in a frying pan. Mix together flour, salt, and cayenne pepper in a small pie dish. Dredge the onion strings in the flour mixture. Shake to remove excess flour and place strings into hot oil. Don’t overcrowd pan or the onion strings will clump together and not get crispy. You will most likely need to do multiple batches to fry all your onion strings. Fry until golden brown and crispy. This takes a few minutes, and you should stir and turn the onion strings as needed to ensure all sides get golden and crisp. Removed from pan and drain on a paper towel lined plate. Taste and sprinkle with a little extra salt, if needed. Top burger with onion string.