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In the mixer bowl, combine the butter, sugar and salt.
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Beat on medium speed until smooth.
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Reduce the speed to low, add the egg yolks and vanilla and beat until blended.
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Add the flour and beat until incorporated and a smooth dough forms.
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Divide the dough into 4 equal portions.
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Roll out each portion into a log 7 inches long and about 1 1/2 inches in diameter.
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Wrap the logs in plastic wrap and refrigerate until firm, at least 2 hours.
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Preheat an oven to 350°F
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Line 3 baking sheets with parchment paper or a silicone baking mat.
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Using a sharp knife, cut each unwrapped log crosswise into slices 1/4 inch thick.
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Place the cookies 1 inch apart on the prepared baking sheets.
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Bake the cookies, 1 sheet at a time, until the edges and bottoms are golden, 12 to 15 minutes.
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Let the cookies cool on the baking sheets for 5 minutes, then transfer them to wire racks and let cool completely.
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Store in an airtight container at room temperature for up to 5 days. Makes about 65 cookies.