Preheat the oven to 325 degrees F. and line your baking sheets with parchment paper.
Add the butter and the brown sugar to the bowl of your stand mixer and beat on medium speed until the mixture is light and fluffy, around 2 minutes.
Add the egg and vanilla and beat for another minute. Add the flour, sprinkle in the baking soda, baking powder, and salt. Mix until combined. Add the oats and combine. The mixture will be a little tacky, but you should be able to roll it into a ball in your hands without making a total mess. If it is too sticky, add 1 tablespoon of flour at a time until the mixture can be handled.
Roll the dough into 1 to 1.5-inch balls, using your hands, and place the balls on the prepared cookie sheet 2 inches apart. Bake for 10 to 14 minutes until the edges begin to brown and the centers are set. Transfer to a wire rack and let them cool completely.
For the filling, beat the butter and vanilla together until light and fluffy, about 2 minutes. Add the powdered sugar and beat for another 2 minutes. Gently fold in the marshmallow cream.
When the cookies are cooled, match them with a mate according to size. Take one cookie and place a few tablespoons of the filling in the center on the flat bottom of the cookie. Take the mate and place it on top (flat sides together) and press it until the filling comes to the edge of the cookies.
Enjoy with lots of milk -- they are rich!
Notes
The cookies continue softening because of the frosting filling over time so that they may get softer and chewier after a couple of days.
They'll last for up to 4 months frozen in an airtight container.
They're sweetened to perfection and make cookie sandwiches something you'll always want in your life.
To make these gluten-free, substitute gluten-free flour and GF oats for regular and old-fashioned oats.