Heat unsalted butter in a large skillet over medium-low heat. Add thinly sliced yellow onions and brown sugar, stirring to coat. Cook slowly for 25-30 minutes until deep golden brown and jammy, stirring occasionally.
Meanwhile, combine ground beef, Worcestershire sauce, garlic powder, onion powder, smoked paprika, salt, and black pepper in a large bowl. Mix gently just until combined.
Remove caramelized onions from heat and let cool slightly. In a small bowl, mix mayonnaise, sour cream, minced garlic, lemon juice, salt, and pepper. Stir in cooled caramelized onions and adjust seasoning to taste.
Prepare vegetables by washing and chopping lettuce, dicing tomatoes and cucumber, and thinly slicing red onion. Arrange separately for easy assembly.
Heat olive oil in a large skillet over medium-high heat. Add seasoned ground beef, breaking it up with a wooden spoon. Cook for 8-10 minutes until browned and cooked through, stirring occasionally but allowing good browning.
Remove cooked beef from heat and let rest briefly. Taste and adjust seasoning if necessary.
To assemble bowls, place a generous base of lettuce in each serving bowl. Top with warm cooked ground beef.
Arrange diced tomatoes, cucumber, sliced red onion, and pickle slices around the beef in sections for visual appeal.
Add a generous dollop of caramelized onion aioli over each bowl. Sprinkle shredded cheddar cheese and chopped fresh chives on top.
Serve immediately with extra aioli on the side.