1. Heat oven to 425° F. Place the potatoes in a large pot and add cold water to cover.
2. Bring to a boil and add 1 teaspoon salt. Reduce heat and simmer until just tender, about 15 minutes. Drain the potatoes and return them to the pot.
3. Add the milk, butter, and ¼ teaspoon each salt and pepper to the potatoes and mash.
4. Meanwhile, heat the oil in a large skillet over medium-high heat. Add the beef and cook, breaking it up with a spoon, until browned, 5 to 6 minutes.
5. Stir in the ketchup, Worcestershire sauce, ½ teaspoon salt, and ¼ teaspoon pepper. Add the peas and carrots.
6. Transfer the beef mixture to 4 individual baking dishes and top with the mashed potatoes. Bake until golden brown, 15 to 20 minutes.
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