01 -
Melt butter in a large skillet over medium heat. Add the sliced onions and cook, stirring every few minutes, for 12–15 minutes until soft and golden brown. If the onions begin to brown too quickly, reduce the heat.
02 -
Stir in the balsamic vinegar, brown sugar, and a pinch of salt. Continue cooking, stirring occasionally, until the liquid reduces to a glossy, syrupy consistency. Transfer to a bowl and set aside.
03 -
Shape ground beef into 4 equal patties. Season both sides generously with salt and pepper.
04 -
Heat a grill or skillet over medium-high heat. Cook the patties for 3–4 minutes per side, or until desired doneness is reached.
05 -
During the last minute of cooking, place a slice of provolone on each patty and cover to allow the cheese to melt.
06 -
Toast burger buns lightly if desired. Spread mayonnaise onto the base of each bun, add a handful of arugula, top with a beef patty, and finish with a generous spoonful of balsamic caramelized onions. Cap with the top bun and serve immediately.