Combine butter, brown sugar, and white sugar in a large bowl; beat with an electric mixer until smooth creamy, 3 to 5 minutes. Beat in egg, 1 tablespoon milk, and 1 teaspoon vanilla extract.
Mix oats, flour, cocoa powder, cinnamon, baking soda, baking powder, and salt together in a separate bowl. Beat into the creamed butter mixture on low speed. Fold in chocolate chips using a rubber spatula.
Cover bowl with plastic wrap and refrigerate dough until firm enough to scoop, at least 1 hour.
Preheat oven to 375 degrees F (190 degrees C). Line 2 baking sheets with parchment paper.
Scoop small balls of dough onto the lined baking sheets using a small cookie scoop.
Bake in the preheated oven until golden, about 10 minutes. Let cookies sit on the baking sheets for 2 minutes. Transfer to a wire rack to cool completely.
Combine cream cheese and vegetable shortening in a bowl; beat with an electric mixer until smooth. Add marshmallow cream, 2 teaspoons milk, and 1/2 teaspoon vanilla extract; mix well. Beat in confectioners' sugar, 1/4 cup at a time, until filling reaches a thick consistency.
Scoop some of the filling onto the flat side of 1 cookie using the cookie scoop. Press another cookie on top to sandwich the filling. Repeat with remaining cookies and filling.