In the bowl of a stand mixer, cream together the butter and brown sugar for about 2 minutes, until light and fluffy.
Preheat the oven to 350F. Line a baking sheet with a silicone liner or parchment paper.
Add eggs and vanilla, mixing into the butter mixture until completely combined. Scrape the sides of the bowl as necessary.
In a separate bowl, combine oats, flour, cinnamon, baking soda and salt. Whisk them together to evenly distribute the spices and aerate the flour.
Turn the stand mixer on low and add the oat mixture to the wet ingredients, until just combined.
Use a 2-tablespoon cookie scoop to drop the cookie dough onto the prepared baking sheet. You should end up with about 35 cookies.
Bake for 8-11 minutes, until lightly golden around the edges. Do not overbake, they should be soft.
Allow cookies to cool on a wire rack while you prepare the frosting.
Beat the butter in the bowl of a stand mixer until light and smooth.
Add both jars of marshmallow fluff to the butter and cream on medium speed until smooth.
Put the mixer on low and slowly add powdered sugar until incorporated, then increase speed back up to medium and beat until smooth and light.
Each level of cake should contain about 7 cookies. Arrange the first layer on the serving cake stand or plate. If you need to overlap them, it's fine.
Top with buttercream. Keep repeating until all the cookies and all the frosting are used. Be generous with the frosting on the lower layers. End with buttercream at the top of the cake.