In a large deep skillet, melt one tablespoon butter and oil over medium-low heat. Add onions, kosher salt and pepper and cook until caramelized, stirring often, for about 35-40 minutes.
While the onions are cooking, to a large pot, combine potatoes, two tablespoons of salt and enough water so the potatoes are covered by at least one inch. Bring to a boil and then reduce to a low boil for 15-20 minutes until potatoes can be pierced easily with a fork. Drain potatoes and return them to the pot. Toss them around in the hot pot to dry the potatoes out.
In a small microwavable bowl, combine the remaining 4 tablespoons of butter and milk and heat until the butter is melted. You can also cook on the stovetop instead of the microwave.
Using a potato masher slightly mash your potatoes. Add half of the milk mixture and continue to mash. Add the remaining milk mixture and mash the potatoes until smooth. (I like to leave in some lumps, but do what you prefer)
Gently fold in some of your caramelized onions. Transfer the potatoes to a serving bowl and fold in the remaining caramelized onions. Dot the top with an extra tablespoon or two of butter and sprinkle with chopped chives, if desired.