In a large mixing bowl, beat the butter and sugars together until light and the mixture comes together, about 5 minutes. Add the egg and beat until well incorporated. Add the milk and vanilla and beat until smooth.
In a separate bowl, whisk together all remaining ingredients except the vanilla cream. Add to the butter mixture and stir by hand until the dough comes together (it should be well incorporated but not overly mixed). Place in the refrigerator to chill for at least 1 hour or up to 12 hours.
Heat the oven to 375°F. Once the dough has chilled, drop rounded teaspoonfuls about 2 inches apart onto a baking sheet. Bake until golden brown but soft in the center, about 10 minutes. Remove to a wire rack to cool completely.
Once the cookies have cooled, match them in pairs. (You want cookies of roughly the same size and shape.) Turn one cookie upside down and place approximately 1 tablespoon of the vanilla cream on the underside of it (which is facing up). Place the second cookie on top of the cream, baked side up. Press the two sides together gently to even out the cream filling. Continue this process with the remaining cookies.
Beverage pairing:Young’s Double Chocolate Stout, England. This dark, chocolaty confection of a beer is kept from being too sweet by the hops and dark roasted malt, making for a rich but not cloying drink. It will add flavor and textural complexity to this simple, satisfying dessert.