Position an oven rack in the center of the oven and preheat to 350°F (175°C). Line two baking sheets with parchment paper and set aside.

In a medium bowl, whisk together the flour, ground ginger, cinnamon, baking soda, salt, and nutmeg. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and brown sugar. Mix on low speed until blended, then increase to medium speed and beat until light and fluffy, approximately 3 minutes.

Add the egg and vanilla extract to the butter mixture and beat until fully incorporated.

In a separate bowl or measuring cup, whisk together the sour cream, molasses, and vegetable oil until smooth.

With the mixer on low speed, alternately add the flour mixture and sour cream mixture to the batter, beginning and ending with the flour mixture. Mix just until incorporated, avoiding overmixing.

Drop the batter by tablespoonfuls onto the prepared baking sheets, spacing each portion approximately 2 inches apart.

Bake one baking sheet at a time for approximately 10 minutes, or until the cakes spring back lightly when touched. Allow the cakes to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

To prepare the filling, place the butter and shortening in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until smooth and combined.

Add the marshmallow crème, dark rum, nutmeg, and powdered sugar. Beat on low speed until incorporated, then increase to medium speed and beat until light and fluffy, approximately 3 minutes.

To assemble, pipe or spread the filling onto the flat side of one cooled cake. Top with a second cake, flat side down. Repeat with the remaining cakes.