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To prepare the COOKIES:.
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Sift dry ingredients together and set aside.
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In a large bowl, with mixer on medium speed,cream butter, and sugar till blended and lightened in color, 2-3 minutes.
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Stop and scrape down sides and bottom of bowl as needed during mixing.
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Add the egg and vanilla and mix till blended, about 1-2 minutes.
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On low speed, add flour mixture and mix just until incorporated and batter looks smooth.
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Cover and refrigerate the dough for about 20 minutes to firm it slightly.
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Position a rack in the middle of the oven.
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Preheat oven to 325F and line two sheets with parchment paper; set aside.
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Roll heaping tablespoons of dough between the palms of your hands until smooth 1 1/2-inch balls and place them 3 1/2 inches apart on prepared baking sheet.
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Using the palm of your hand, flatten the cookies to 2 1/2 - 3 inch rounds.
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Bake the cookies, one sheet at a time until the tops feel firm and look dull rather than shiny, about 15 minutes.
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Cool cookies on cookie sheet for 5 minutes before transferring them to rack to cool completely.
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To prepare the CHOCOLATE COATING:.
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Put both chocolates and oil in top of double boiler over barely simmering water in bottom boiler.
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Stir until the chocolate is melted and smooth.
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Remove from the water and let the chocolate cool and thicken slightly before spreading, about 20 minutes.
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Spoon the chocolate coating over the top of half of the cookies.
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Use the back of a small spoon to spread the chocolate evenly and coat them completely.
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You will probably have a small amount of chocolate coating left over.
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Let the cookies sit at room temperature until the chocolate is firm--or to speed the firming, refrigerate for 20 minutes and then remove them from the refrigerator.
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To prepare the FILLING:.
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In large bowl, combine butter and powdered sugar and vanilla and peppermint extract until smoothly blended about 1 minute.
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The filling will be quite thick Turn plain cookies bottom side up and spoon rounded tbs of filling in center of each.
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Carefully place the bottom of a chocolate covered cookie on top and gently press together to spread the filling in an even layer.
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The filling will not reach the edges.
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Wrap each cookie in plastic wrap and store in refrigerator for at least 2 hours.
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Serve cold -- the wrapped cookies can be stored in refrigerator up to 4 days.
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Try them frozen -- !