Place an oven rack in the second highest position and preheat the broiler to high. Coat a 9x13 baking dish with cooking spray. Set aside.
Add potatoes to a large pot of cold water and bring to a boil over high heat. Boil 15 minutes or until tender. Drain, return to the pot, and stir over medium heat for 30 seconds until most of the water has evaporated. Remove from the heat and mash, adding the butter, milk, ¾ cup of the parmesan cheese, and salt and pepper to taste.
Once the potatoes are smooth and free of lumps, spread evenly into the prepared baking dish. Sprinkle with the remaining parmesan cheese. Broil 5-10 minutes or until the top is just beginning to brown. Sprinkle with fresh rosemary if desired.
To make the red wine balsamic reduction
While the potatoes are broiling, prepare the red wine balsamic reduction by adding all ingredients to a small saucepan and bringing to a boil. Boil 15 minutes or until reduced by half and slightly thickened. Transfer to a gravy boat or similar serving dish and pour the reduction over individual servings of the mashed potato bake.
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