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Split the vanilla bean with a sharp knife and scrape out the seeds.
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Beat the unsalted butter and a scant cup of powdered sugar until smooth.
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Add the egg yolk until just combined.
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Beat in the salt and the vanilla bean seeds.
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Beat in the flour gradually until just combined
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Gather the dough into a ball and wrap it in plastic cling film.
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Refrigerate for at least 2 hours.
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Preheat the oven to 350 degrees F.
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Line two baking sheets with parchment paper.
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Pinch off a small section of the dough, and rewrap the rest. Place it back in the refrigerator.
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Roll the dough out into a long rope on a lightly floured surface,
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Pinch off a section at a time and form into pretzel shapes.
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Place the pretzel shapes on the baking sheets.
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Place on the middle rack in the oven. Bake for 10-15 minutes just until they start to brown slightly. Remove from the oven and immediately transfer to a wire rack lined with parchment paper to cool completely.
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Whisk together the egg white with the rum, lemon juice, and remaining powdered sugar.
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Use a small pastry knife to spread the rum glaze on the cookies.
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Let the glaze dry completely before transferring to a serving platter.