In a medium bowl, whisk together mayonnaise, ketchup, mustard, minced pickled okra, okra brine, vinegar, garlic powder, salt, and pepper until well combined. Set aside.

Thinly slice the yellow onion and cut the jalapeños into rings, removing seeds for a milder flavor if preferred.

Portion the ground beef into 2.5-ounce balls, keeping the beef loosely shaped.

Preheat a skillet to 425-500°F (220-260°C).

Toast the brioche buns cut-side down on the skillet until golden brown, about 1-2 minutes.

Season the beef balls with kosher salt and black pepper, then smash each ball firmly into a thin patty on the hot skillet. Cook for 1-1.5 minutes until a crust forms.

Top the patties with sliced onions and jalapeños. Flip and cook for an additional 30-45 seconds.

Place a slice of American cheese over a patty, stacking another on top. Let the cheese melt for about 30 seconds.

Spread prepared sauce on the cut side of the top bun. Layer with the stacked patties and toppings, then cap with the bottom bun.