Preheat the oven to 350 degrees F and line a baking sheet or two with parchment paper.
In a medium bowl, combine the flour, lemon zest, baking soda, and salt and whisk together.
In a stand mixer (or large mixing bowl), beat the butter until creamy. Add the sugar and beat until fluffy and light. Add the egg and beat until it is mixed and combined. Add the vanilla and combine. On low speed, add the flour mixture and buttermilk in batches, alternating and starting and ending with the flour.
Onto the cookie sheets, drop level tablespoons about 1 ½ inches apart. If lumpy, shape into balls with your fingers before baking. Bake about 11-15 minutes per batch. Remove and let cool on a wire rack.
For the glaze, first make the raspberry syrup. Heat the lemon juice and raspberries over low heat. Smash raspberries with a spoon as they soften. After about 5 minutes, remove from heat and strain through a mesh strainer to remove any seeds and so you are left with a raspberry liquid.
Take the sifted powdered sugar and add the buttermilk and 3 tablespoons of the raspberry liquid. Whisk to combine until smooth and a glaze forms. Spoon the glaze onto the cookies and allow the cookies to sit until the glaze is set.