Prepare the toppings:
In a medium skillet, heat the olive oil over medium heat. Add the sliced onions and cook, stirring occasionally, until they begin to soften and brown, about 10-12 minutes. Sprinkle the brown sugar over the onions and continue cooking for another 3-4 minutes until they caramelize. Stir in the white vinegar and cook for an additional minute, then remove from heat.

Prepare the patties:
Form the ground beef into 4 equal portions, rolling them into balls. Season each ball with a pinch of salt and pepper.

Cook the burgers:
Heat a large cast-iron skillet or griddle over high heat until very hot. Place the beef balls in the pan, and using a spatula or a burger press, smash each ball down to form a thin patty. Sear for 2-3 minutes until the edges are crispy and golden. Flip the patties, and immediately place a slice of cheese on top of each one. Let the cheese melt as the burgers cook for another 2 minutes.

Toast the buns:
While the burgers are cooking, butter the insides of the burger buns and toast them in a separate pan over medium heat until golden brown.

Assemble the burgers:
Place the cooked smash patties on the bottom half of the toasted buns. Top each patty with a generous spoonful of caramelized onions and a few slices of jalapeños. Add pickles if desired, and top with the other half of the bun.

Serve and enjoy:
Serve immediately with your favorite sides—fries, chips, or a simple salad!