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COOKIES:
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Combine butter and sugar in a in a mixer and beat until very smooth and creamy, apx. 3 minutes. Add egg and vanilla; mix well. Sift flour and baking powder in a separate bowl and with the mixer on low add in. Beat until well mixed.
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Divide dough into thirds, mound into rounds in plastic food wrap, flattening slightly. Refrigerate until firm (2 to 3 hours).
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Once well chilled taking one round out at a time, roll onto a well floured surface to about 3/16th thick. The dough is very soft and forgiving. Using cookie cutters cut out any shapes desired. Ball together the scraps and repeat.
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Place cut-outs onto parchment lined baking sheets and bake cookies at 400 degrees for 6 minutes, until just very lightly browned at the bottom edge.
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Transfer onto a cooling rack and once cooled frost with buttercream frosting.
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FROSTING:
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In a mixer beat softened butter at high speed until very light and fluffy (3 minutes). On low begin to add 10X sugar, this may create a coarse texture, blend until incorporated, then one tablespoon full at at time add milk until a soft fluffy consistency is achieved.
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Using a teaspoon or an offset spatula, spread onto cooled butter cookies.
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For best results, refrigerate frosted cookies for 1 hour to set.