Heat oven to 375°F. Line 3 large baking sheets with parchment paper. In a medium bowl, whisk together the flour, baking powder, salt and baking soda.

Using an electric mixer, beat the butter, sugars and lemon zest in a large bowl until light and fluffy, about 3 minutes. Reduce the mixer speed too low and beat in the egg. In two additions, alternately add the flour mixture and buttermilk, mixing just until incorporated. Gently fold in the berries.

Scoop 32 mounds of batter (about 1 ¹/² Tbsp each) onto the prepared baking sheets, spacing them 2 inches apart. Bake in batches until puffed and the tops spring back when lightly pressed, 12 to 14 minutes. Let cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely.

Form sandwiches with the cold pies and ice cream (about 2 Tbsp per sandwich).