Line a baking sheet with foil and set aside.
Place the ground turkey in a large mixing bowl and add the onion, mushrooms, ¼ cup barbecue sauce, and Cajun seasoning. Use clean hands to combine the mixture well.
Divide the mixture into 6 even-sized balls and place them on the prepared baking sheet. Use your hands to flatten them into ½ to ¾-inch patties. If making ahead, cover the baking sheet with plastic wrap and place in the refrigerator. (Note - refrigerating the patties makes them hold together well. Burgers should be cooked within 24 hours.)
When ready to cook, preheat your outdoor or indoor grill or place a skillet over MEDIUM HEAT. Gently lift each turkey patty and spray both sides with non-stick cooking spray. Transfer to the grill (or skillet) and cook for 5 to 7 minutes, per side, or until the exterior of the burgers is nicely seared and they register an internal temperature of 165 degrees F.
Discard the foil from the baking sheet and replace it with a clean sheet of foil for the cooked burgers.
Baste the tops of the burgers with additional barbecue sauce, if desired. Add cheese, cover the grill, and cook for just a minute or two until the cheese has melted.
Serve on hamburger buns with Awesome Burger Sauce and your toppings of choice.