Heat a skillet over medium heat with the butter and oil.
Add the onions to the skillet. Cook the onions until they have softened, about 5 minutes.
Turn down the heat to medium-low. Continue to cook, stirring occasionally, until the onions have turned a deep brown color, approx. 20-30 minutes. If the onions start to dry out, turn down the heat or add a splash of water or beef broth. Also, a pinch or two of sugar can be added to assist with the caramelization if desired.
Let the onions cool slightly.
Meanwhile, in a mixing bowl, combine the sour cream, mayonnaise, and seasonings. Stir in the cooled onions.
Serve immediately or refrigerate several hours or overnight. Store the dip covered in the refrigerator for up to four days.