In a small mixing bowl, combine the Greek yogurt, yellow mustard, dill pickle relish, garlic powder, onion powder, and paprika to create the special sauce.
Divide the ground beef into two equal portions and press them into very thin, wide patties.
Season both sides of the beef patties evenly with sea salt and black pepper.
Heat a non-stick skillet or cast-iron pan over medium-high heat and sear the patties for 2 to 3 minutes per side until a deep brown crust forms.
Place the half slice of cheddar cheese on one of the patties during the final minute of cooking, covering the pan briefly to help it melt.
Lightly toast the whole wheat bun in the same skillet or a toaster until golden and warm.
Assemble the burger by spreading half of the special sauce on the bottom bun, followed by shredded lettuce, diced white onion, and dill pickle slices.
Stack the two beef patties on top of the vegetables, spread the remaining sauce on the top bun, and serve immediately.