01 - Heat butter and olive oil in a large skillet over medium heat. Add sliced onions, salt, and sugar. Cook, stirring occasionally, for 20-25 minutes until onions are deep golden brown and fully caramelized, lowering heat as needed to prevent burning. Remove from heat and set aside.
02 - In a mixing bowl, gently combine ground beef with salt, pepper, and garlic powder. Divide meat into 8 equal portions and shape into small patties, making them slightly larger than the slider buns to account for shrinkage during cooking.
03 - Heat a grill pan or skillet over medium-high heat. Cook patties for 2-3 minutes per side for medium doneness, adjusting time for preferred doneness level.
04 - During the final minute of cooking, place a cheese slice on each patty. Cover the pan with a lid to allow cheese to melt completely.
05 - Lightly butter cut sides of slider buns and toast in a skillet or on a griddle until golden brown and crispy.
06 - Spread mayonnaise and/or Dijon mustard on bottom buns if desired. Place cheese-topped patties on buns, top generously with caramelized onions, and add lettuce, tomato, or pickles if using. Cover with top buns and serve immediately.