Melt the butter in a 12-inch skillet over medium heat. Add onions, salt, pepper, and cayenne and cook, stirring occasionally, until the onions are translucent, about 10 minutes. Reduce the heat to medium-low and continue cooking until the onions are golden, about 10 more minutes.

Add 2 tablespoons of the water to the skillet and cook, scraping up any browned bits, until the water is evaporated, about 5 minutes. Add the remaining 2 tablespoons water and cook until onions are caramelized and water is evaporated, about 5 minutes longer. Remove from heat and stir in the vinegar. Transfer the onions to a medium bowl and allow to cool for at least 10 minutes.

Add the sour cream and mayonnaise to the onions and stir to combine. Season with salt and pepper to taste. Refrigerate for at least 30 minutes (and up to 24 hours) to allow flavors to blend. Serve with your favorite potato chips.