Make the cookies: Preheat oven to 400 degrees. Sift together flour, salt, cocoa powder, baking soda, and baking powder. Set aside. Line 2 baking pans with parchment paper. In the bowl of an electric mixer fitted with the paddle attachment, cream butter and sugar until light and fluffy. Add eggs, buttermilk, and vanilla. Beat until well combined. Slowly add dry ingredients. Mix until combined.

Using a 1-ounce ice cream scoop, place dough onto a parchment-lined baking pan, 12 per pan. Bake for 10 to 12 minutes. Remove to a rack to cool. Repeat with remaining batter.

Make the vanilla buttercream: In the bowl of an electric mixer fitted with the paddle attachment, cream butter until smooth and creamy, 2 to 3 minutes. With mixer on low speed, add 3 cups sugar, milk, and vanilla; mix until light and fluffy. If necessary, gradually add remaining cup sugar to reach desired consistency.

Transfer buttercream to a disposable pastry bag and snip the end. When cookies have cooled completely, pipe 2 tablespoons buttercream onto the flat side of half the cookies. Sandwich with remaining cookies, pressing down slightly so that the filling spreads to the edge of the cookies.