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Preheat oven to 375°F and place rack in middle.
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In a large frying pan, bring 1 cup of beef broth to a simmer. Gradually add meat a few slices at a time until it is no longer pink, then set aside. Repeat with remaining meat, adding a bit more broth as needed.
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Once all the meat is cooked, add tea to remaining liquid in pan and bring to a light boil.
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Mix cornstarch into ½ cup of cold water until well blended.
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Slowly add mixture to pan while stirring constantly until sauce thickens. Let simmer a few minutes before returning all meat to the pan.
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Season generously with salt and pepper to taste.
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Pour meat filling into a large Pyrex or lasagna pan (approx. 9" x 13" [23 cm x 33 cm]) and spread it out evenly.
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Roll out your pie dough and cut into large strands approximately 1" (2.5 cm) wide. Place them across the pan in a crisscross or braided pattern.
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Bake for approximately 20 to 25 minutes until crust is golden and cooked through.
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Serve with a salad or your favourite side.