Preheat oven to 375°F. Line a baking sheet with parchment.
Place the butter in the bowl of a stand mixer. Using a paddle attachment, mix on medium speed until creamy. Scrape down the sides of the bowl.
Add sugar, zest, and salt, and mix until combined, about 2 minutes.
Add vanilla and mix until combined. Scrape down the bowl.
Add flour and mix on medium-low until the dough begins to come together.
Dump dough on the counter and use your hands to knead the dough together into a ball.
Roll the dough into a square that is about 1/2 inch thick and wrap it in plastic. Refrigerate for half an hour.
Place the dough between two sheets of parchment paper and roll out until it is 1/4” thick. If it is too firm, let it rest for a few minutes.
Cut the dough into desired shape using a knife or cookie cutter.
Place cookies on a parchment-lined baking sheet and bake for 13-15 minutes or until the bottoms are lightly golden. Allow cookies to cool to room temperature.