Heat the oil in a 12-inch skillet over medium heat until shimmering. Add the carrots and onion and cook over medium heat until the vegetables are softened, 6-8 minutes.
Stir in the beef or cubed meat and cook, breaking up ground beef chunks with a wooden spoon, until no longer pink, about 5 minutes. Stir in the flour, garlic and tomato paste and cook for 1 minute. Gradually whisk in the broth, worchestershire and thyme.
Bring the mixture to a simmer over medium-low heat and cook, stirring occasionally, until thickened but still saucy, 15-20 minutes. Off the heat, stir in the peas and corn and season with salt and pepper to taste.
Slice open each baked potato and sdd a pat of butter to each potato. Top with 1/6 of the shepherd's pie mixture and serve.
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