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Preheat oven to 425 degrees. In a large skillet, cook meat, onion and carrots together, stirring occasionally, until vegetables are softened and meat is cooked through, 5-8 minutes.
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Add the tomato paste, stirring to combine, then sprinkle the flour on top. Cook, stirring frequently, for 2 minutes.
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Add Worcestershire sauce, water, salt and pepper. Simmer, stirring occasionally, about 10 minutes, until mixture is thickened.
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Stir in peas; cook 1 minute longer. Pour into a good-size casserole dish (mine is about 6x11).
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In a medium saucepan, bring water to a boil. Add potatoes and cook over medium-low heat until tender, 15 to 20 minutes. Drain.
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Return potatoes to pan, add milk and butter, mash to combine and until potatoes are reasonably smooth. Season with salt and pepper, adding more if needed. Spread over the meat mixture; use a fork to make little peaks.
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Bake on a baking sheet until the top is golden-brown, 25 to 30 minutes. Cool slightly and serve warm.