In a large bowl using a mixer, beat softened butter with granulated sugar until fluffy. Add in vanilla extract, beat until smooth. Add in flour and beat until all of the flour is incorporated.
Beat in milk. Cover and refrigerate dough for at least one hour. Preheat oven to 350 F. Roll cookie dough into balls and place 2-inches apart onto ungreased baking sheets. Bake for 10-12 minutes. Place powdered sugar in a shallow dish, roll baked cookies in powdered sugar.