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In the bowl of electric mixer,beat together the butter, sugar and salt, then add the rum, beat until you obtain a fluffy mixture.
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Stir in the sifted flour and mix to obtain a smooth texture.
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Cover and chill for 1-2 hours.
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Preheat the over to 350°F.
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Roll the dough into 1-inch balls, which you place 1-inch apart on ungreased baking sheets, and bake 10-12 minutes(firm but not brown), then transfer to a wire rack and cool.
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Prepare the filling:.
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Melt the chocolate and butter together and stir until smooth. Cool slightly.
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Spread a small amount of the chocolate on the bottom of a cookie,and cover with another cookie like a sandwich and press gently. Repeat with remaining cookies. Cool until filling is set.
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Store for up to 1 week.