Prepare the caramelized onions:
Heat olive oil and butter in a large skillet over medium heat. Add the sliced onions and a pinch of salt. Cook slowly, stirring occasionally, for about 25–30 minutes until the onions turn golden brown and soft. Add brown sugar and balsamic vinegar during the last 5 minutes of cooking to enhance the flavor. Set aside.

Make the beef patties:
In a large bowl, combine ground beef with Worcestershire sauce, garlic powder, onion powder, smoked paprika, salt, and pepper. Mix just until combined—avoid over-mixing to keep the patties tender.

Shape the sliders:
Divide the beef mixture into 12 equal portions and form into small patties about the size of your slider buns. Make a slight indentation in the center of each patty with your thumb to prevent puffing during cooking.

Cook the patties:
Heat a grill, grill pan, or cast-iron skillet over medium-high heat. Cook the patties for 2–3 minutes on each side, or until your desired doneness. In the last minute of cooking, place a half-slice of cheese on each patty and cover the pan to melt the cheese.

Toast the buns:
While the patties cook, lightly toast the slider buns on a grill or skillet until golden.

Assemble the sliders:
Spread a thin layer of mayonnaise and/or Dijon mustard on the bottom half of each bun if desired. Place the cooked patty with melted cheese on the bun, top with a generous spoonful of caramelized onions, and add any other toppings like lettuce, tomato, or pickles. Cover with the top bun.

Serve immediately:
Arrange the sliders on a platter and serve hot. Perfect with crispy fries, coleslaw, or a simple side salad.