Preheat the oven to 180°C / 350°F / Gas mark 4.
Line 2 baking trays with greaseproof paper and set aside.
In a food processor or using an electric beater, mix the butter and granulated sugar until fluffy.
Add the egg yolks, vanilla, and salt and mix to combine.
Gradually add the flour, mixing until just incorporated.
Divide the dough in half and shape into 5cm diameter logs.
Wrap in baking paper and refrigerate until firm, about 30 minutes.
Slice the logs into cookie thick pieces and space them apart on the prepared baking trays.
Bake until lightly golden, 15 to 20 minutes.
Let cool on the baking trays 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 halfway into the glaze and let set, about 15 minutes.
Wrap for gifts or serve.