How to Make It
In a medium bowl, using a hand mixer, beat the butter with the granulated sugar at medium speed until light and fluffy, about 3 minutes. With the machine on, beat in the eggs and egg yolks 1 at a time. Beat in the lime juice, lemon juice and salt; the mixture will curdle.
Scrape the curd mixture into a medium saucepan and cook over moderately low heat, stirring constantly, until it’s thickened and reaches 180° on an instant-read thermometer, about 10 minutes. Strain the curd through a fine sieve into a medium bowl. Press a sheet of plastic wrap directly on the surface of the curd and refrigerate until firm, at least 3 hours or overnight.
Line 2 baking sheets with parchment paper. In a medium bowl, whisk the flour with the lime zest and salt. In another medium bowl, using a hand mixer, beat the butter with the confectioners’ sugar at medium speed until light and fluffy, about 3 minutes. Beat in the vanilla, then beat in the dry ingredients just until combined. Stir in the cranberries. On a lightly floured surface, roll out the dough 1/4 inch thick, then cut into 2-inch squares and transfer to the baking sheets. Refrigerate for 1 hour.
Preheat the oven to 350°. Bake the cookies for about 20 minutes, shifting the pans halfway through baking, until golden. Transfer the cookies to a rack and let cool. Serve with the lime curd.