Preheat oven to 350 degrees. Line 2 baking sheets with parchment paper and set aside.
In a large bowl, cream butter and sugar together until light and fluffy. Stir in egg, vanilla and lemon zest. Scrape sides and whip again. Measure out all dry ingredients and pour into batter. Slowly mix while streaming in sour milk. Stir until just combined. Scrape sides and mix again by hand to ensure batter is smooth and evenly mixed. Scoop onto prepared baking sheets and bake 6-9 minutes or until bottoms of cookies are barely browned.
While cookies are baking, stir lemon juice and sugar together to make the glaze. Once cookies come out of the oven, immediately spoon glaze over top hot cookies. Cool 3 minutes and remove cookies onto cooling rack. Serve. Store any extra cookies in airtight containers for up to 3 days.