Melt the butter in a large skillet over medium heat. Add the onions and 1/2 tsp of the salt and cook, stirring every few minutes, for 25-30 minutes, until soft, deep golden brown and jammy. If the pan looks dry or the onions start to stick, add a splash of water and scrape up the browned bits.
Stir in the garlic powder and cook for 30 seconds, then stir in the Worcestershire sauce and scrape the pan. Spread the onions on a plate and let them cool for 10 minutes.
In a medium bowl, whisk the Greek yogurt, mayonnaise, Dijon mustard and pepper until smooth.
Fold in the cooled onions, cover, and refrigerate for at least 1 hour, or up to 3 days.
Just before serving, stir in most of the chives and taste for salt; chilling mutes the seasoning, so adjust now rather than earlier.
Scatter the remaining chives over the top and serve with cucumber spears, carrot sticks, pita chips or potato chips.