Fill a large pot with water. Add a generous amount of salt and the bay leaf. Bring to a boil and then add the potatoes. Cover and let boil for 15-20 minutes (depending on the size of your potatoes) until fork tender. Remove the potatoes from the boiling water, and peel and rice them.
While the potatoes are boiling, melt 3 tablespoons of butter in a medium-sized (preferably nonstick) saucepan over low heat. Turn the heat up to medium and add the diced onions as well as a large pinch of salt. Cook for 10 minutes, and then add another tablespoon of butter. Continue to cook until the onions have caramelized (golden-brown), about another 10 minutes. Stir frequently to make sure all the onion is evenly caramelized and nothing is burning. Remove the caramelized onions from the saucepan and set aside.
Fill a medium-sized saucepan (it can be the same one you cooked the onions in) with 1 cup of water. Add the sliced carrots and bring the water to a boil. Then, reduce the boil to a simmer and let the carrots cook for 8-10 minutes, or until tender. Strain all the water from the pan, reserving the carrots (the easiest way to do this is with a colander).
Over low heat, add one tablespoon of softened butter to a medium-sized saucepan (again, it can be the same one). Let melt, and then add the brown sugar and a pinch of salt. Mix together until combined and the sugar is dissolved, 2-3 minutes. Add the carrots back to the pan, coating them in the glaze. Remove the glazed carrots from the pan and set aside.
Combine the riced potatoes, caramelized onions, glazed carrots, cream cheese, 3 tablespoons softened butter and chopped chives in a bowl and mix the ingredients together. Once mixed, add the scalding milk and mash all the ingredients together. It’s helpful to use a masher, pushing it to the bottom of the bowl and rocking it back and forth to mash carrots and onions underneath into even smaller pieces. It shouldn’t look homogenous, but the butter and cream cheese should be fully incorporated and most of the carrots and onions should be somewhat mashed. Add salt and pepper to taste and mix. Serve.