Thinly slice and separate the two yellow onions. Heat the vegetable oil and butter in a large, heavy skillet over medium heat, then add the onions, kosher salt, black pepper, and optional cayenne.

Cook the onions for 8 to 10 minutes, stirring frequently, until they soften. Reduce the heat to low or medium-low and continue cooking for 20 to 35 minutes, stirring periodically, until deeply golden brown and sweet.

If the skillet becomes dry or the onions begin to stick or scorch, stir in 1 tablespoon of water. Remove the onions from the heat and let them cool completely before mixing them into the dairy base.

For a smoother dip, finely chop the cooled onions. Beat the softened cream cheese, sour cream, and mayonnaise in a bowl until smooth, then stir in the onions and optional Worcestershire sauce or garlic powder.

Refrigerate the finished dip for at least 30 minutes. Bring it close to room temperature before serving, and finish with chopped chives or green onions if desired.