1 hour 30 min (90 mins)
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In a large bowl, mash together the bread and 1⁄2 cup of milk. Gently knead in the meat, 2 teaspoons of salt, and 10 grinds of pepper, mixing well. Heat half of the butter in a large, heavy saucepan over medium-high heat. When the butter has melted, add the meat-bread mixture, pushing down with a wooden spoon, and brown, 10 to 11 minutes. Add the onions, carrots, parsnips, and finely chopped garlic, and sauté until the onions have softened, about 3 minutes. Add the tomato paste and flour and stir until the flour disappears, about 1 minute. Remove the pan from the heat, add the wine, and then cook for 1 to 2 minutes, stirring. Add the tomatoes and rosemary and bring to a boil, about 2 minutes, gently mashing the tomatoes with a potato masher. Carefully pour into the slow cooker, cover, and cook on low until the flavors are blended together, 4 to 6 hours. Remove and discard the rosemary sprigs and—using a large ladle or spoon—skim the grease off the surface.
Meanwhile, place the root vegetable chunks in a medium-size saucepan, cover with cold water by about 2 inches, and salt generously. Bring to a boil over high heat, then cover and reduce to a simmer over medium low; simmer until very tender, about 15 minutes. Meanwhile, add the remaining 11⁄2 cups milk, remaining garlic, the nutmeg, remaining 2 tablespoons butter, 1⁄2 teaspoon salt, and 8 grinds pepper to a small saucepan. Bring to a simmer over medium-high heat. Drain the root vegetables over a colander in the sink, then pour the root vegetables back into the dry pot. Mash with a potato masher, pouring in the milk mixture. Stir until a smooth purée forms.
Heat the oven to 400°F. Place a 9x13x2-inch baking dish on a rimmed baking sheet. Ladle the meat filling into the baking dish. Cover with the root vegetable mash, spreading evenly. Sprinkle evenly with cheese. Bake until the cheese melts, the potatoes turn golden brown, and the meat sauce thickens, 25 to 30 minutes. Serve.