For the Cookies – Preheat oven to 325°F and line two baking sheets with Silpat liners or parchment paper; set aside. In a large mixing bowl, combine first 11 ingredients, up to the salt, and whisk until smooth. Add the remaining ingredients, and mix until just combined; don’t overmix. Batter will be soft and runny.
Using a one-quarter cup measure, scoop the batter onto prepared baking sheets, six round mounds of batter per sheet; this may also be done with a pastry bag if preferred.
Bake for about 12 to 14 minutes, or until tops have set. Cookies will be very soft and may look underdone, but firm up as they cool. Allow cookies to cool on baking sheets for at least 10 minutes before moving them to rack to finish cooling. Allow cookies to cool completely before filling and sandwiching them together. While they cool, make the filling.
For the Buttercream Filling – To the bowl of a stand mixer fitted with a whisk attachment, combine the milk, vanilla extract, and 1 cup of the powdered sugar, then mix on high speed until the mixture is creamy and light. Add butter and remaining cup of sugar, and whip on high speed until very light, about 8 to 10 minutes.
Apply a generous dollop of frosting to 6 of the cookies. Sandwich them together with the remaining unfrosted 6 cookies, creating 6 whoopie pies. Whoopie pies are best fresh, but extras may be stored airtight in the refrigerator (due to the buttercream) for about 3 days. If you prefer to keep them at room temperature, the frosting may be made with 1/4 cup vegetable shortening instead of butter.