Heat oil in a large nonstick frying pan over medium heat. Add onions and cook, stirring occasionally, until brown, sticky, and caramelized, about 20 minutes. If it seems to be starting to burn, reduce heat to medium-low and add 1 tablespoons water, stirring well.

Transfer onions to a small bowl and chill until cold, about 1 hour.

Reserve a heaping tablespoon of the caramelized onions for a garnish.

In a food processor, pulse remaining onions, sour cream, buttermilk, and salt just until combined.

Transfer to a serving dish, top with reserved onions, and chill at least 1 more hour. It can be made ahead for up to two days and kept chilled.