Cream butter, brown sugar, and granulated sugar until light and fluffy.
Beat in eggs one at a time, then vanilla.
Whisk flour, oats, baking soda, cinnamon, and salt together, then mix into the wet ingredients until just combined.
Preheat oven to 350°F. Scoop dough into balls and bake for 9 to 11 minutes, until edges are set and centers look slightly soft.
Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Beat softened butter until smooth, add marshmallow fluff and beat until combined, then add powdered sugar, vanilla, and salt, beating until fluffy.
Pipe or spoon filling onto one cookie, top with a second cookie, and press gently until filling spreads to the edges.