Preheat oven to 350°F with a rack in the upper third and lower third of the oven. Line two baking sheets with parchment paper.

In a food processor, pulse the oats several times, until broken down into small pieces but not powdery. Add flour, cinnamon, baking soda, and salt and pulse a few more times until combined.

Using a hand mixer or stand mixer fitted with the paddle attachment, beat butter, brown sugar, and granulated until creamy and combined. Add eggs, molasses, and vanilla extract and beat until combined, scraping the sides and bottom of the bowl as necessary. Add the dry ingredients and beat until fully combined. Allow the dough to sit at cool room temperature for 5 minutes.

Scoop the dough into 1½ tablespoon balls and place a couple inches apart on the baking sheet. Bake for 9-11 minutes, until the edges are beginning to set but the center is still underdone. Place the baking sheets on wire racks and allow the cookies to cool completely.

Using a hand mixer or stand mixer fitted with the paddle attachment, beat butter until smooth. Add marshmallow creme and beat until combined. Add powdered sugar, ½ cup at a time, followed by vanilla and salt. Beat until fully combined.

Add the frosting to a piping bag fitted with a large round tip. Squeeze some frosting onto the underside of a cookie and immediately top with another cookie. Repeat.