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Whisk together flour, baking soda, salt, and spices in a medium bowl.
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Beat butter and sugar with a mixer on medium-high speed until fluffy. Add eggs, 1 at a time, beating well after each addition. Beat in honey and molasses. Reduce speed to low. Gradually add flour mixture, and beat until just combined. Divide dough into 3 portions, and wrap each in plastic. Refrigerate for 1 hour.
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Preheat oven to 350 degrees. On a generously floured piece of parchment, roll dough to a scant 1/4 inch thick. Brush off excess flour. Slide dough and parchment onto a baking sheet, and freeze for 15 minutes.
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Cut out desired shapes. Transfer to parchment-lined baking sheets, and freeze for 15 minutes.
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Bake cookies for 6 minutes. Remove sheets from oven, and tap them firmly on counter to flatten cookies. Return to oven, rotating sheets, and bake until crisp but not darkened, 6 to 8 minutes more. Let cool on sheets on wire racks.
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Spoon icing into a pastry bag fitted with a very small plain round tip (such as Ateco #0 or #1). Pipe designs on cookies. Let cookies stand at room temperature until set, at least 2 hours (preferably overnight).
Cook’s Notes
Cookies can be stored between layers of parchment in airtight containers for up to 1 week.
