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Preheat oven to 350F. Line a 9-inch cake pan with parchment paper.
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In a bowl, combine ground chicken, hot dogs, and egg. Transfer to the prepared pan and spread with fingers.
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Bake in preheated oven for about 40 minutes, or until the meat is cooked through.
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While the cake is cooking, boil the diced sweet potatoes until fork tender, about 20 minutes. Strain and beat with an electric mixer until mostly smooth.
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Cool the cake completely before spreading the mashed sweet potatoes on top and serving.