Caramelize the onions: Heat olive oil and butter in a large heavy skillet (preferably cast iron) over medium heat. Add the diced yellow onions and 1/2 teaspoon kosher salt. Cook, stirring occasionally, for 10 minutes until softened and translucent.

Develop deep golden flavor: Reduce heat to medium-low. Continue cooking for 25 to 30 minutes, stirring every few minutes, until the onions are deeply caramelized, jammy, and golden brown. If the pan browns too quickly, stir in 1 tablespoon of water to deglaze and scrape up all flavorful brown bits. Remove from heat and cool completely (at least 15 minutes).

Mix the creamy base: In a medium mixing bowl, whisk together the sour cream, Greek yogurt, garlic powder, onion powder, Worcestershire sauce, and cracked black pepper until silky smooth.

Fold and chill: Reserve 1 tablespoon of caramelized onions for garnish. Fold the remaining cooled caramelized onions into the creamy base until evenly distributed. Cover and refrigerate for at least 1 hour (or up to 24 hours) to allow the rich savory flavors to meld completely.

Garnish and serve: Transfer dip into a serving bowl. Top with the reserved caramelized onions and chopped fresh chives. Serve cool with crisp wavy potato chips, artisan crackers, or fresh vegetables.