Lemon Buttermilk Cookies

1. Line 2 large baking sheets with parchment paper or silicone liners. Preheat the oven to 350°F.
2. In a medium bowl, whisk together the flour, zest, baking soda, and salt.
3. In a large mixing bowl, beat the butter briefly, until creamy. Add the sugar, and beat until pale and fluffy. Add the egg, and beat well to mix. Add the vanilla, and beat briefly again. Slowly mix in the flour mixture and the buttermilk in batches, beginning and ending with the flour. Scrape down the sides of the bowl with a rubber spatula as needed. The finished dough should be smooth and pale yellow.
4. Drop the dough by level tablespoonfuls onto the prepared baking sheets, leaving about 1 ½ inches between each cookie. Bake, 1 sheet at a time, until the cookies are puffed and their edges are golden, about 11 to 15 minutes per batch. Cool the cookies on the baking sheet for 1 minute; then transfer them to a wire rack.
5. To prepare the glaze, whisk together the sifted confectioners sugar, buttermilk, and vanilla. The mixture should be very smooth, with no lumps of sugar visible. Brush or spoon the glaze onto the warm cookies. Allow cookies to sit on the rack until they are fully cooled and the glaze is set.