Peel and thinly slice the onions. Add the sliced onions to a 12-inch non-stick skillet along with water, olive oil, and ½ teaspoon of salt.
Turn the heat up to high. After the water starts boiling, cover the skillet with a lid, reduce medium-high heat, and cook for ten minutes.
Remove the lid, stir, and allow the onions to continue cooking for 15 more minutes, stirring with a wooden spoon every few minutes.
Cook for another 15 minutes until the onions have started to significantly reduce, stirring every few minutes. If the onions begin to get too dry on the bottom of the pan, add a few tablespoons of water and stir.
Next, lower the heat to medium and cook until the onions are golden brown and have a sweet, jammy consistency.
Once the onions are a deep golden caramel color and have reduced to ½ - ¾ cups, remove them from the heat and set aside.
Next, combine the Greek yogurt, mayo, garlic powder, onion powder, Worcestershire sauce, the remaining ½ teaspoon of salt, and pepper in a mixing bowl.
Add the caramelized onions and chopped chives and stir to combine. Chill the dip, covered in plastic wrap, for at least one hour or overnight. Remove the plastic wrap, stir, and garnish with freshly chopped chives just before serving.