01 - Melt butter with olive oil in a large skillet over medium heat. Add sliced onions and salt, stirring to combine. Cook for 5 minutes, then add sugar. Continue cooking, stirring frequently, until onions become deep golden brown and soft, approximately 20 minutes. Remove from heat and set aside.
02 - In a mixing bowl, gently combine ground beef, kosher salt, black pepper, Worcestershire sauce, and garlic powder. Divide mixture into 8 equal portions and shape each into a small patty slightly larger than the buns, allowing for shrinkage during cooking.
03 - Heat a grill pan or skillet over medium-high heat. Cook patties 2 to 3 minutes per side until browned and cooked to desired doneness. During the final minute, place a cheese slice on each patty and cover to allow cheese to melt.
04 - Slice buns in half. Butter cut sides if desired. Toast cut sides down in a skillet or on the grill until golden brown.
05 - Spread mayonnaise and/or Dijon mustard on bottom halves of buns if using. Layer with lettuce leaf and tomato slice if desired, followed by cheesy beef patty and a spoonful of caramelized onions. Add pickles if preferred and cap with top bun.
06 - Serve sliders hot immediately after assembly.