Preheat the oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt; set aside.
In a large bowl or the bowl of a mixer fitted with the paddle attachment, beat 6 tablespoons butter, the cup of sugar, and 1 teaspoon lemon zest on medium speed until smooth, about 3 minutes.
Add the egg, 1 tablespoon lemon juice, and 1 teaspoon vanilla and mix until combined.
Reduce mixer speed to low and add half of the flour mixture, then the 1/2 cup buttermilk, then the remaining flour; mix just until combined.
Drop heaping tablespoons of batter onto the prepared sheets about 3 inches apart to form rounds.
Bake for 10 to 12 minutes, until the tops are set and cookies feel firm; remove from oven and cool on the sheets for 10 minutes, then transfer to a wire rack to cool completely.
To make the filling, beat 6 tablespoons butter and 6 ounces cream cheese in a mixer with the paddle attachment until smooth, then add 1 teaspoon vanilla, 1 teaspoon lemon zest, and 2 tablespoons lemon juice and mix to combine.
Add the 2 3/4 cups powdered sugar and beat until the filling is smooth and spreadable.
Assemble whoopie pies by placing a large dollop of filling on the underside of half the cookies, top with the remaining cookies, and chill briefly to set before serving.