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Whisk together flour, coffee, baking powder, baking soda, and salt in a bowl.
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Cream shortening and butter in a large mixing bowl. Add sugar and brown sugar and beat until light and fluffy.
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Add egg and rum and beat until combined.
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Add dry ingredients and mix until just combined. The dough will appear crumbly.
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Divide dough in half. Push together each half and roll into logs 2 inches in diameter. Wrap each log in wax or parchment paper and chill overnight.
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Preheat oven to 400 degrees F. Line baking sheets with parchment or non-stick liner.
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Remove paper from dough logs and cut dough into 1/8 inch slices.
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Place slices 1 inch apart on baking sheets. Gently press a pecan half into the center of each slice.
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Bake for 7 to 9 minutes, until the edges are light brown.
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Watch the cookies beginning at the 6 minute mark and be careful not to over-bake. They will brown very quickly.
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Immediately transfer cookies to a wire rack and cool completely.
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Cool cookie sheets completely between batches.