In a medium bowl, use an electric mixer to beat the butter and granulated sugar until fluffy. Add egg yolks, vanilla, and salt. Beat to combine. Gradually add the flour, mixing until just incorporated. Divide the dough in half and shape into 1 inch-diameter logs. Wrap in waxed paper and refrigerate until firm, about 30 minutes.
Preheat the oven to 350 degrees.
Slice the dough logs into ¼-inch-thick pieces and place 1 inch apart on parchment-lined baking sheets. Bake until lightly golden, around 18 minutes. Let cool on baking sheets, then transfer to cooling racks.