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 the pan starts to burn, reduce heat to medium-low and add 1 tbsp. water, stirring well. Transfer onions to a small bowl and chill until cold, about 1 hour.
Reserve 1 tbsp. onions. 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 hour.
Make ahead: Up to 2 days and chill.
Note: Nutritional analysis is per 2-tbsp. serving.