In a small bowl, whisk together the nonfat Greek yogurt, yellow mustard, and sugar-free pickle relish to create the secret sauce.
Place the center-cut bacon slices in a cold skillet and turn the heat to medium, cooking until the fat has rendered and the bacon is crispy.
Remove the bacon to a paper towel-lined plate, leaving about a teaspoon of the rendered fat in the pan for flavor.
In a medium bowl, gently mix the ground beef with garlic powder, onion powder, sea salt, and black pepper until just combined.
Form the beef into two equal, thin patties approximately 4 inches in diameter.
Increase the skillet heat to medium-high and sear the patties for 3 minutes on the first side until a deep, golden crust forms.
Flip the patties; immediately place the sharp cheddar cheese slice on one patty and stack the second patty directly on top of the cheese.
Cover the pan with a lid for 1 minute to allow the cheese to melt completely and the beef to reach your desired level of doneness.
Lay out the large butter lettuce leaves on a plate and place the double patty stack in the center.
Top the patties with the crispy bacon, tomato slices, and red onion slices.
Finish with a generous dollop of the secret sauce before wrapping the lettuce leaves tightly around the burger to serve.