Zucchini Whoopie Pies with Cream Cheese Frosting

MAKE CAKES:

Preheat oven to 350°F with racks in upper and lower thirds. Butter 2 large baking sheets.

Squeeze handfuls of zucchini that have been wrapped in a kitchen towel in order to remove moisture. Set aside.

Whisk together flour, baking soda, spices, and salt until combined. Set aside.
Whisk together buttermilk and vanilla in a small bowl. Set aside.

Beat together butter and brown sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 5 minutes. Add egg and beat until combined well. At low speed, mix in flour and buttermilk mixtures alternately in batches, beginning and ending with flour mixture and mixing until smooth. Mix in zucchini just until incorporated.

Spoon 1/4-cup mounds of batter 2 inches apart onto the prepared baking sheets. Bake, switching position of sheets halfway through, until tops are puffed and golden and spring back when touched, 18 to 22 minutes. Transfer with a spatula to a rack to cool completely.

MAKE FILLING:

Beat together cream cheese, butter, confectioners sugar, vanilla, rum and salt with cleaned beaters at medium-high speed until smooth, about 3 minutes.

ASSEMBLE PIES:
Spread a rounded 2 Tablespoons of filling on the flat sides of half of the cakes and top with remaining cakes.