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1
Beat butter at medium speed with a heavy-duty electric stand mixer until creamy; gradually add sugar, beating unil light and fluffy.
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2
Add egg and vanilla, beating until blended, scaping bowl as needed.
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3
Combine flour, baking soda, and salt; gradually add flour mixture to butter mixture, beating at low speed until blended.
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4
Divide dough into 2 equal portions.
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5
Roll 1 portion of dough into a 12x8 inch rectangle on a piece of lightly floured plastic wrap.
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6
Knead food coloring paste into remaining portion of dough while wearing rubber gloves.
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7
Roll tinted dough into a rectangle as directed in step 3.
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8
Invert untinted dough onto tinted dough; peel off plastic wrap.
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9
Cut dough in half lengthwise, forming 2 12x4 inch rectangles.
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10
Roll up each rectangle, jelly-roll fashion, starting at 1 long side, using bottom piece of plastic wrap as a guide.
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11
Wrap in plastic wrap, and freeze 4 hours or up to 1 month.
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12
Preheat oven to 350 degrees.
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13
Cut ends off each dough log, and discard.
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14
Cut dough into 1/4 inch thick pieces, and place on parchment paper lined baking sheets.
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15
Bake at 350 degrees for 6-7 minutes or until puffed and set; cool cookies on baking sheets for 5 minutes.
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16
Remove to wire racks and cool completely (about 30 minutes).
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17
Make the frosting: Beat butter and cream cheese at medium speed with an electric mixer until creamy.
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18
Gradually add powdered sugar, beating at low speed until blended.
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19
Increase speed to medium, and gradually add milk and peppermint extract, beating until smooth.
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20
To assemble: Place Peppermint Frosting in a heavy-duty zip-top plastic freezer bag.
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21
Snip 1 corner of bag to make a small holw.
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22
Pipe about 2 teaspoons frosting onto half of cookies; top with remaining cookies, gently pressing to form a sandwich.
