Preheat oven to 350 degrees and lightly grease 2 baking sheets.
Using an electric mixer, cream shortening and brown sugar.
Add eggs, one at a time, beating well after each addition.
Combine flour, cinnamon, baking soda, salt, and nutmeg and add to mixture. Beat just until combined.
Stir in oats.
Drop batter by rounded teaspoonfuls onto prepared baking sheets. Place in oven and bake until golden brown, about 10-12 minutes. (You will have to bake multiple batches.)
Let cool on baking sheets 3 to 5 minutes and then remove to wire racks to cool completely.
To make filling, use an electric mixer to beat shortening, sugar, and marshmallow creme until smooth.
Beat in enough milk to get desired consistency.
Spread filling on the bottom of half of the cookies and top with remaining cookies.