Wash and slice the lettuce, tomato, cucumber, pickles, and onion. Keep the toppings refrigerated until needed.
Place the ground beef in a large bowl. Add the egg, yogurt, salt, black pepper, and garlic powder. Mix until evenly combined.
Add the breadcrumbs and gently mix them into the meat. Let the mixture rest for 10 minutes so the breadcrumbs can absorb the excess moisture. If it remains too soft, add 1-2 additional tablespoons of breadcrumbs.
Combine the mayonnaise, mustard, ketchup, and sour cream in a small bowl. Add a grated pickle or a few drops of lemon juice if desired. Refrigerate until serving.
Divide the meat mixture into four equal portions. Using a burger press lined with parchment paper, shape each portion into a large, even patty. You can also shape the patties by hand.
Heat a large skillet or grill pan over medium heat. Cook the patties until nicely browned on the first side, then flip and cook until fully cooked through. Ground beef patties should reach an internal temperature of 160°F (71°C).
Cut the burger buns in half and lightly toast or warm the cut sides in a clean skillet.
Spread the creamy burger sauce over both halves of each bun. Layer the pickles, cooked burger patty, cucumber, lettuce, tomato, and onion on the bottom half.
Cover with the top half of the bun and serve immediately while warm.
