Preheat an oven to 325°F.
In a food processor, combine the flour, the 1/3 cup granulated sugar, the confectioner’s sugar, lemon zest and salt and process briefly to blend. Add the butter and process just until the mixture resembles coarse meal. Turn the dough out onto a floured work surface and gather it into a rough ball.
Roll out to a 1/4 inch thickness and cut as desired. You may use cookie cutters, cut them in squares, or use a fluted rotary cutter like I did mine.
Bake about 10-15 minutes until blond, but not golden brown. I like a soft cookie. You may like it more crunchy, if so bake till golden brown.