Add first 7 ingredients under 'toppings' (through cayenne) to a blender or food processor; blend until smooth. Pour sauce into a sealable dish and refrigerate until ready to serve. (Not into heat? Leave out the cayenne.)
Spray a large skillet with cooking spray; heat over medium. Mix ground turkey and beef in a glass bowl until combined; shape into 4 patties. Season each side with salt and pepper. Place burgers into hot skillet and cook for 2-3 minutes per side or until edges begin to crisp and center is no longer pink.
While burgers cook, heat a second skillet over medium. Open buns and spread insides with butter. Place each bun open side down onto hot skillet. Toast for 1 minute. Spread each bun with pre-made sauce; set aside.
When burgers are finished cooking, remove skillet from heat and immediately add cheese to each burger to melt. Transfer burgers to buns. Top each off with lettuce and a few slices of tomato.