Peel potatoes and cut into cubes. Place in cold salted water and bring to a boil, reduce heat to low boil until potatoes are fork tender, about 15 minutes. Drain potatoes and mash with milk and 2 tablespoons of the butter until smooth. Season with salt and pepper to taste and set aside. Brown ground beef in a large saucepan over medium-high heat. Remove ground beef from pan and drain off excess fat, reserving 3 tablespoons of fat. Put reserved fat in saucepan add onion, carrot, and celery. Sweat for 5 minutes until onion becomes translucent, add mushrooms, and frozen peas saute for 5 more minutes. Return ground beef to pan along with parsley, thyme, Worcestershire, and nutmeg, simmer for 1 to 2 minutes. Add brown gravy to pan simmer 1 to 2 minutes, season to taste with salt and pepper. Remove from heat and let cool. Preheat oven to 400 degrees. Layer bottom of a 3-liter casserole dish with beef mixture, top with mashed potatoes making uneven peaks with a fork. Cut remaining butter into small cubes and sprinkle over mashed potatoes. Bake for 30 to 40 minutes until mashed potatoes have turned golden brown, remove from oven and let cool 5 minutes.
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