Stack two baking sheets together and line the top with parchment paper. You will need to repeat this for each batch.
In a mixer bowl, using a whisk attachment, whisk egg yolks and sugar until thick and pale, 1 to 2 minutes. Slowly blend in softened butter and vanilla.
Gradually add flour and salt, blending until dough is thick and stiff. If it is still quite soft add a bit more flour, a few tablespoons at a time. Knead dough gently and briefly on a lightly floured work surface. Then wrap dough well and refrigerate 45 minutes.
Preheat oven to 325°F
On a lightly floured surface, roll dough to 3/4 inch thickness. Cut into 3 inch round cookies and place on prepared baking sheet. With tines of a fork make a criss cross pattern on the dough.
For glaze, in a small bowl whisk egg yolks with water. Brush each cookie generously with egg wash mixture.
Bake until golden on top and browned around the edges, 50 to 55 minutes. Let cool completely on baking sheets.