Preheat oven to 375 degrees F. Line two baking sheets with parchment paper.

In a medium bowl, sift together the flour, baking powder, baking soda, and salt; set aside.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter, shortening, and sugar until fluffy, about 3 minutes.  Add egg and egg white, and beat until incorporated.  Add half of flour mixture and half of milk to creamed mixture; beat at medium speed just until blended.  Add remaining half of flour, milk and vanilla; beat until blended. Fold in sprinkles.

Drop by heaping tablespoons of the dough onto the prepared baking sheets, about 2-inches apart. Bake, one baking sheet at a time, until cakes begin to crack and are firm to the touch, 10 minutes.  Remove from oven and slide the parchment paper, with the cakes, onto a wire rack to cool completely.  Use a thin metal spatula to lift the cookies off the parchment paper.

To make the filling: In the bowl of a stand mixer fitted with the paddle attachment, beat together the marshmallow fluff and the vegetable shortening, on medium speed until the mixture is smooth and fluffy, about 3 minutes.

Add the confectioners’ sugar and the vanilla and beat on low until incorporated. Increase mixer speed to medium and beat until fluffy, about 3 minutes more.

To assemble, turn half of the cooled cookies upside down, flat side facing up. Drop a large dollop of filling onto the flat side of the cookie, leaving a 1/4-inch plain edge.

Place another cookie, flat side down, on top of the filling. Press down slightly so that the filling spreads to the edges of the cookie.

Roll edges in sprinkles. Repeat until all cookies are used.