Begin by heating a large skillet over medium-low heat and add the butter, allowing it to melt slowly with a gentle sizzle.
Add the thinly sliced sweet onions to the skillet and stir them into the melted butter, coating them evenly. Cook slowly, stirring occasionally, for about 30-40 minutes, until the onions are deeply golden and soft, filling the kitchen with a sweet, caramelized aroma.
Sprinkle in the salt and stir to distribute, helping the onions develop their rich flavor and color as they continue to cook for another 5 minutes.
Remove the skillet from heat and transfer the caramelized onions to a mixing bowl. Let them cool slightly until they are warm to the touch, but not hot.
Add the sour cream to the cooled onions and mix thoroughly, combining until the mixture is smooth and velvety with a rich, golden hue.
Adjust the seasoning with additional salt if desired and transfer the dip to a serving bowl.
Serve the caramelized onion dip with chips, bread, or vegetable sticks, and enjoy its deep, sweet-savory flavor with a creamy, smooth texture.