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.