01 - In a large skillet over medium heat, melt butter with olive oil. Add sliced onions, salt, and sugar. Cook, stirring occasionally, for 20–25 minutes until onions are deep golden brown and fully caramelized. Lower heat as needed to prevent burning. Set aside.
02 - In a bowl, gently mix ground beef with salt, pepper, and garlic powder. Divide into 8 equal portions and shape into small, slightly larger-than-bun patties (they will shrink as they cook). Heat a grill pan or skillet over medium-high heat. Cook patties for 2–3 minutes per side for medium, or to desired doneness.
03 - During the last minute of cooking, place a slice of cheese on each patty. Cover pan to melt cheese.
04 - Lightly butter and toast slider buns, cut sides down, in a skillet or on a griddle until golden.
05 - Spread mayonnaise and/or Dijon mustard on the bottom bun, if desired. Place the beef patty with melted cheese on the bun. Top with a generous spoonful of caramelized onions. Add lettuce, tomato, or pickles if using, then cover with top bun. Serve immediately.