Put the potatoes in a medium saucepan, cover with cold water and add a generous pinch of salt. Bring to a boil, reduce to a simmer and cook until the potatoes are tender but not falling apart, about 15 minutes. While the potatoes cook, combine the milk and 6 tablespoons of the butter together in a small saucepan and heat over medium, stirring, until the butter melts and the milk is steaming. Drain the potatoes and return to the saucepan over medium heat. Add the warm milk mixture and mash the potatoes until just slightly chunky. Season with salt and pepper and set aside.
Heat the olive oil in a large skillet over medium heat. Add the onion, carrots, celery, mushrooms, garlic, oregano, 1 teaspoon salt and a few grinds of pepper. Cook, stirring, until vegetables are tender, about 10 minutes. Stir in the tomato paste and cook until the mixture turns brick red, about 2 minutes. Add the beef and 1/2 teaspoon salt. Continue to cook, breaking up the meat with a spoon into small pieces, until no longer pink, about 4 minutes. Add the beef broth and Worcestershire sauce and cook until saucy, about 1 minute more. Remove from the heat.
Transfer the beef mixture to a 2-quart oval casserole dish and top with the mashed potatoes. Swirl decoratively with a spoon, stopping about 1/4-inch from the edge of the dish. Melt the remaining tablespoon of butter and drizzle over the potatoes. Bake until the potatoes are brown and the filling is bubbly, about 40 minutes. Sprinkle with parsley.
Copyright 2016 Television Food Network, G.P. All rights reserved.