1 ½lbsrusset potatoespeeled and cut into 1-inch cubes
½lbsweet potatoespeeled and cut into 1-inch cubes
½cupheavy whipping cream
Salt and freshly ground black pepper to taste
Adjust oven rack to upper middle position and preheat oven to 375°.
Brown ground beef in a large skillet. Remove from skillet, drain and set aside.
In the same large skillet, heat olive oil over medium heat. Add yams, onions, and carrots and cook, stirring frequently until everything is tender. Add mushrooms and cook until mushrooms soften and release their juices.
Sprinkle flour over everything, and then squirt in ketchup. Stir and cook over medium-low heat for about one minute.
Add cream and cook about another minute. Add wine or juice, Worcestershire sauce, and thyme. Simmer over medium heat, stirring frequently, until mixture is thick but still saucy, 5-8 minutes.
Add browned ground beef to the mixture in skillet and stir to combine. Pour mixture into a 2-quart casserole dish.
In a large saucepan over high heat, bring potatoes, sweet potatoes, 1/2 teaspoon salt, and water to cover to boil. Reduce and simmer until tender, 15-20 minutes; until tender.Drain potatoes. Add butter and cream to potatoes and mash until smooth. Season with salt and pepper.
Carefully spread prepared potatoes over meat and vegetable filling, using a spatula or large spoon to smooth the top. In a small bowl, make an egg wash by whisking together 1 tablespoon water with egg. Brush the top of the potatoes with egg wash, and then drag a fork across the top to make ridges. Put in oven and bake until the filling is bubbling, about 15-20 minutes.
Turn on broiler and cook until top is golden brown, 3-5 minutes. Remove and cool 10 minutes. Serve.
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