For cookies, beat butter and sugar together until light and fluffy and stir in lemon zest. Beat in egg yolks and whole egg until fully incorporated. Stir in crème fraiche or sour cream until smooth. In a separate bowl, sift flour, baking powder, baking soda and salt. Add to wet ingredients and stir just until blended. Chill batter for 30 minutes, just to set butter a little.
Preheat oven to 325 °F. Spoon tablespoons of batter (an ice cream scoop works great) onto a parchment lined cookie sheet, leaving 2 inches between cookies. Bake for 15 to 18 minutes, just until the bottoms of the cookies turn golden brown. Allow to cool before icing.
For icing, stir sifted icing sugar into lemon juice until smooth. Stir in melted butter (this will thicken the icing a bit). Dip the tops of the cookies into icing, and place on a cooling rack, so excess icing can drip off. Let cookies set 1 hour before removing, and store in an airtight container, with layers of parchment between the cookies to prevent sticking.
Serve these lemon cake cookies with a tart lemon curd!
Whisk together lemon juice, eggs and yolk, and sugar. Whisk in butter and add lemon zest. Place bowl over a pot of simmering water and whisk steadily, but gently, until curd becomes thick and pale and creamy, about 10-15 minutes. Remove from heat and chill until ready to use.