Preheat oven to 325°F (160°C) and line a baking sheet with parchment paper.
Cream together butter and powdered sugar until light and fluffy.
Add lemon zest, lemon juice, and vanilla extract, mixing until smooth.
Whisk together flour and salt, then gradually fold into the wet mixture until a soft dough forms.
Roll out dough on a lightly floured surface and cut into desired shapes, or scoop and flatten for round cookies.
Place on prepared baking sheet and chill in the refrigerator for 10–15 minutes to prevent spreading.
Bake for 15–18 minutes or until edges are lightly golden.
Cool on the baking sheet for 5 minutes, then transfer to a wire rack. Optional: drizzle with lemon glaze or dust with powdered sugar.