Preheat the oven to 350. In a large bowl, cream together the butter and sugar until light and fluffy. Add the vanilla extract and mix well to combine. Add the flour and mix until the dough comes together. Add milk as needed until the dough reaches the consistency of play dough.
Scoop the dough into a cookie press. Hold the cookie press down on an ungreased, unlined baking sheet, and press to form the cookies. Bake 10-12 minutes, until very lightly golden on the bottom.