In a small mixing bowl, whisk together the Greek yogurt, yellow mustard, sugar-free ketchup, pickle juice, and smoked paprika until the secret sauce is smooth and combined.
Divide the ground beef into two equal portions and gently shape them into thin, wide patties about 4 inches across.
Season both sides of the beef patties evenly with the sea salt and black pepper.
Heat a cast-iron skillet over medium-high heat and add the avocado oil, swirling to coat the surface.
Add the turkey bacon to the skillet and cook for 2-3 minutes per side until it reaches a crispy texture, then remove and set aside on a paper towel.
Place the beef patties in the hot skillet and sear for 3 minutes without moving them to develop a deep brown crust.
Flip the patties and cook for another 2 minutes; place the cheddar cheese slice on one of the patties and cover the skillet with a lid for 30 seconds to melt.
Remove the patties from the heat and lightly toast the sprouted bun halves in the remaining juices in the skillet for 30 seconds.
Assemble the burger by spreading half of the secret sauce on the bottom bun, followed by the lettuce, tomato, onion, both beef patties, and the crispy turkey bacon.
Spread the remaining sauce on the top bun, close the burger, and serve immediately.