In a small bowl, combine all of the sauce ingredients together, mix well, and set aside or refrigerate until ready to use.
In a larger bowl, combine ground turkey, the other half can of the green chiles, salt, pepper, garlic and onion powders, ground cumin, smoked paprika, chili powder, and cayenne pepper. Mix until well combined and seasonings are distributed evenly.
Divide the turkey mixture into 4 equal parts, and form into burger patties. Drizzle a skillet with a small amount of olive oil. Preheat skillet or cook-top on med-high. Cook burgers about 5-7 minutes per side, or until cooked through. Add cheese slices the last minute or two to melt.
Spread Greek yogurt sauce on toasted buns, and assemble burgers with fresh tomato, lettuce, and avocado or guac. Enjoy!