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Preheat oven to 350F. Line 2 baking sheets with parchment paper.
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In a large bowl, beat butter and sugar together until light and fluffy. Beat in egg, red food coloring and peppermint extract.
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In a separate bowl, whisk flour, cocoa, baking powder and salt; gradually beat into the butter mixture.
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Shape dough into 1-inch balls. Place 1 inch apart on prepared baking sheets and use a round teaspoon to make a deep indention in each ball.
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Bake 9-11 minutes or until set. Remove from pans to wire racks to cool completely.
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In a microwave, heat white chocolate chips in 30 second intervals, stirring after each one, until melted and smooth. Spoon a teaspoon of filling into each cookie. Drizzle tops with remaining mixture. Let stand until set.