Dice the sweet onions into 1/4-inch pieces. Melt the butter in a large skillet over medium heat, then add the diced onions and 1/2 tsp salt. Cook for 35-40 minutes, stirring occasionally, until the onions turn deep golden brown and develop a rich, sweet flavor. This slow cooking breaks down the onion's natural sugars and creates the caramelized depth that makes this dip special. In the last minute of cooking, add the balsamic vinegar and stir to combine. Remove from heat and let cool for 5 minutes.
While the onions are caramelizing, combine the Greek yogurt, sour cream, Worcestershire sauce, black pepper, garlic powder, and onion powder in a large bowl. Whisk together until smooth and well combined. I like to add the spices gradually and taste as I go—this way you can adjust the seasoning to your preference since everyone's palate is different.
Once the caramelized onions have cooled slightly, reserve about 1/4 cup of the most caramelized onions for garnish. Fold the remaining caramelized onions from Step 1 into the yogurt mixture from Step 2, stirring gently until evenly combined. Finely chop the fresh chives and fold most of them into the dip, saving some for a fresh garnish on top. Top with the reserved caramelized onions and remaining chives just before serving.