With an electric mixer, beat the butter and granulated sugar until fluffy. Add the egg yolks, vanilla, and salt and beat to combine. Gradually add the flour, mixing until just incorporated.
Divide the dough in half and shape into 1 1/4-inch-diameter logs. Wrap in wax paper and refrigerate until firm, about 30 minutes.
Heat oven to 350° F. Slice the logs into 3/8-inch-thick pieces and space them 1 1/2 inches apart on parchment-lined baking sheets. Bake until lightly golden, 16 to 20 minutes. Let cool on the baking sheets for 5 minutes, then transfer to cooling racks to cool completely.
In a small bowl, whisk together the confectioners' sugar, lemon juice, and zest until it forms a thick but pourable glaze (add more lemon juice if necessary). Dip the top of each cookie into the glaze and let set, about 15 minutes.
To Wrap: Give a nut tin a second life. Wipe it clean with a damp towel, then peel off the label. Tie a bow with extra-wide ribbon to hide any glue remnants. Note: If nut allergies are a concern, use a coffee can instead.
To Freeze: Instead of refrigerating the dough, freeze the logs for up to 2 months. To bake, follow the recipe instructions, cutting and baking the dough from frozen, and use the upper end of the time range.