Heat oil in a Dutch oven set over medium heat. When it shimmers, add onions and salt, and cook, stirring, for 15 minutes. Reduce heat to medium-low and continue cooking, stirring occasionally, for 30 more minutes. The onions will release their liquids during the first 10 minutes of cooking, then collapse and slightly darken in color over time. They’re ready when they are a deep golden color and reduced by over two-thirds of their original volume.

Add 2 tablespoons vinegar, stirring and scraping up any browned bits on the bottom of the pan. Continue cooking over medium-low heat for another 10 to 15 minutes, or until onions are totally soft and a deep nut-brown color. Remove from heat, and set aside to cool, 10 to 15 minutes. You’ll have about ½ cup of onions.

When onions are cool, transfer to a cutting board and roughly chop. Place in a medium mixing bowl, and add remaining vinegar, crème fraîche, yogurt, chives, paprika, salt, and pepper. Stir to combine. Taste, and adjust seasoning. Transfer to a serving bowl, sprinkle with remaining chives, and serve with crudités or potato chips.