Cream the butter and sugar in a mixing bowl using an electric mixer until light and fluffy, about 3-5 minutes.
Add the vanilla extract and mix until incorporated.
Gradually add the flour, mixing on low speed until the dough starts to come together.
If the dough is too crumbly, add milk one tablespoon at a time until it holds together.
Shape the dough into a log or press into a square/rectangle. Roll out to ½ inch thickness if using cookie cutters.
Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.
Preheat the oven to 350°F (175°C).
Place the chilled dough on a baking sheet lined with parchment paper and bake for 15-20 minutes until edges are lightly golden.
Let cool on the baking sheet for a few minutes before transferring to a wire rack.