1. Position a rack in the center of the oven and preheat the oven to 375 degrees F. Line two baking sheets with parchment paper.
2. In a medium bowl, stir together both flours, baking powder, and salt.
3. In the work bowl of a stand mixer fitted with the paddle attachment, beat together the butter, shortening and brown sugar until light and creamy, about 3 minutes. Add the eggs and the buttermilk and beat until combined.
4. In a measuring cup, combine the milk, baking soda, and vinegar. Add the milk mixture to the batter along with the flour mixture and beat on low speed until just combined. Add the vanilla and beat on medium speed for about 2 minutes, until completely combined.
5. Using a spoon, drop about 1 tablespoon of batter onto one of the prepared baking sheets and repeat, spacing them at least 2 inches apart. Bake one sheet at a time for about 10 minutes each, or until the cakes begin to brown. Remove from the oven and let the cakes cool on the sheet for at least 5 minutes before transferring them to a rack to cool completely.
6. Make the Marshmallow Filling: In the work bowl of a stand mixer fitted with the paddle attachment, beat together the Marshmallow Fluff and the vegetable shortening, starting on low and increasing to medium speed until the mixture is smooth and fluffy, about 3 minutes. Reduce mixer speed to low, add the confectioners' sugar and the vanilla, and beat until incorporated. Increase mixer speed to medium and beat until fluffy, about 3 minutes more.
7. Make the Chocolate Ganache Filling: Put the chocolate in a large, heatproof bowl. Heat the cream in a large, heavy saucepan over medium heat just until it bubbles. Pour the hot cream over the chocolate in the bowl and let it sit for about 10 minutes, until the chocolate is melted. Stir with a wooden spoon or spatula until smooth. Allow the mixture to rest at room temperature until firm enough to spread, about 2 hours. You may also refrigerate the mixture for about 30 minutes, until it is firm enough to spread, stirring every 10 minutes.
8. Assemble the whoopie pies: Pipe or spread (whatever your preferred method) a layer of chocolate ganache filling onto the flat side of one of the cakes. Using the same method, top the chocolate filling with the marshmallow filling. Top it with another cake, flat-side down. Repeat with the rest of the cakes and filling.
* Note: I know many people are opposed to vegetable shortening, but it really is a necessary ingredient. It gives the cakes their characteristic lift and lightness, and the rounded shape. It is also a crucial component of the classic marshmallow filling. I can attest to both of these after reviewing my mom's old recipes for gobs!