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Preheat the oven to 350 degrees F (180 degrees C).
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Stir together cake mix, oil, and eggs in a large bowl until mixture comes together as a dough. Roll dough into 48 (1 inch) balls. Press a chocolate kiss, with tip pointed down, into center of each, rolling dough to enclose kiss. Arrange 2 inches apart on ungreased cookie sheets.
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Bake until edges are just set (cookies will be soft set), 6 to 8 minutes. Cool cookies on cookie sheets 5 minutes, then transfer to a wire rack to cool completely.
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For chocolate frosting, cook and stir cocoa powder and butter in a small saucepan over low heat until melted and smooth, about 5 minutes. Remove from heat.
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Stir in confectioner’s sugar and vanilla extract. Stir in hot water, 1/2 teaspoon at a time, up to 2 tablespoons, until desired consistency. Spread frosting over cookies.