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Preheat the oven to 350oF (180oC).
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In an electric mixer fitted with a paddle attachment, mix together the room temperature butter and sugar until they are light and pale in color.
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Add the vanilla.
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In a medium bowl, sift together the flour and salt, then add them to the butter-and-sugar mixture. Mix on low speed until the dough starts to come together. Dump onto a surface dusted with flour and shape into a flat disk. Wrap in plastic and chill for 60 minutes.
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Roll the dough ½-inch thick and cut using cutters.
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Place the cookies on a baking sheet.
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Bake for 18 to 20 minutes, until the edges begin to brown lightly. Allow to cool to room temperature.
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Store in an airtight container for 2 weeks.