Position racks in the center and lower third of the oven and preheat to 375 degrees F. Make the cookies: Whisk the flour, baking powder, salt and baking soda in a medium bowl. Beat the butter, sugar and vanilla on medium-high speed in a stand mixer fitted with the paddle attachment until light and fluffy, about 5 minutes. Beat in the egg until combined, scraping down the bowl. Reduce the mixer speed to low and beat in the flour mixture and milk in 3 alternating batches. Fold in the blueberries with a rubber spatula.
Line 2 baking sheets with parchment paper; coat with cooking spray. Arrange mounds of batter, about 2 tablespoons each, 2 inches apart; smooth the tops with a damp finger. Chill until firm, 30 minutes.
Bake the cookies until lightly golden, rotating the pans halfway through, 10 to 12 minutes. Let cool on the pans for 5 minutes, then transfer to a rack to cool completely.
Make the filling: Beat the cream cheese, butter, lemon zest and juice, vanilla and salt with a mixer on medium speed until smooth. Beat in the confectioners' sugar on low speed until combined.
Assemble the whoopie pies: Spread 2 tablespoons of filling on the flat side of 6 cookies and sandwich with the remaining cookies. Serve immediately or refrigerate, covered, overnight.