Well, you make oatmeal cream pies, of course! I found a recipe that doesn't have a lot of sugar - with all that buttercream you don't need an overly-sweet cookie.
Oatmeal Cream Pies
Makes about 7 good-sized pies
1/2 cup (1 stick) butter, softened
2/3 cup light brown sugar, packed
1 large egg
1/2 teaspoon vanilla extract
3/4 cup flour
1/2 teaspoon baking soda
1/2 teaspoon cinnamon
1/4 teaspoon salt
1 1/2 cups rolled oats
Leftover buttercream frosting, about 2 cups (or less)
In a large bowl, cream together the butter, brown sugar, egg and vanilla until smooth. In a separate bowl, whisk the flour, baking soda, cinnamon and salt together. Stir this into the butter/sugar mixture. Stir in the oats.
The cookies should be two inches apart on a parchment-lined baking sheet. Dip the flat bottom of a glass in flour and gently press each cookie flat on top. You'll need to re-flour after every press. Bake them for 10-12 minutes, taking them out when golden at the edges but still a little undercooked-looking on top. Let them sit on the hot baking sheet for five minutes before transferring them to a rack to cool.
Match the cookies up according to size so they pair well. Let cool completely before dolloping buttercream on them and sandwiching them together. It's best to chill them a bit to let the buttercream harden slightly.
Recipe - omitting raisins and nuts - adapted from here.