Preheat the oven to 400°F (200°C). Arrange hash brown patties in a single layer at the bottom of a 9x13-inch baking dish.

Bake the hash browns until golden and crisp on the bottom, about 25 minutes.

While the hash browns bake, grate or finely mince 2 tablespoons of onion and set aside with any accumulated juices. Dice the remaining onion.

In a bowl, combine grated onion, mayonnaise, 1/2 teaspoon salt, sweet pickle relish, white vinegar, sugar, mustard, paprika, and onion powder. Mix well and set aside.

Heat olive oil in a large skillet over medium-high heat. Add ground beef and cook undisturbed for 3 minutes. Crumble the meat with the back of a spoon and cook, stirring occasionally, until browned and mostly cooked through, about 5 minutes.

Season the beef with remaining salt, pepper, Worcestershire sauce, and chopped onions. Cook for 1 minute, then remove from heat and stir in 2/3 cup of the sauce mixture and 1 1/3 cup grated cheese.

Flip hash brown patties over. Pour the beef mixture over the hash browns and top with the remaining grated cheese. Sprinkle with sesame seeds.

Bake until bubbly and cheese is melted, 10 to 12 minutes. Remove from oven and let stand for 5 minutes.

Top with shredded lettuce and drizzle with the remaining sauce. Sprinkle chopped pickles on top and serve immediately.