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In a small bowl, combine the flour and salt. Set aside.
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In a large bowl, beat the butter until smooth. Add the sugar and vanilla and beat until combined.
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Gradually add the flour mixture, beating just until combined.
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Divide the dough in half and roll out each half between two sheets of parchment paper until about ¼ inch thick.
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Wrap the dough in the parchment paper, place on a baking sheet, and place in the refrigerator until firm, about 30 minutes.
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Remove dough from the refrigerator and place on a flat surface. Remove the top piece of parchment paper. Dip the cookie stamp into flour and shake off any excess. Press the stamp into the dough. Use the round cookie cutter to cut out the cookies around the stamp.
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Repeat the cookie stamping and cutting with both halves of the dough.
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Transfer cut out cookies to a parchment lined baking sheet and place in the refrigerator for 15 minutes. While the cookies are chilling, preheat the oven to 350 F.
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Bake the cookies for 10 minutes or until the edges are lightly browned.
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Let the cookies cool on the pan for a couple minutes before carefully transferring to a wire rack to cool completely.