Preheat the oven to 400 degrees F and line a large baking sheet with parchment paper or a silpat liner (very important for these cookies!)
In a large bowl, cream together the softened butter, brown sugar, and white sugar until light and creamy. Beat in the eggs and vanilla extract.
In another bowl, mix together the flour, oats, baking soda, baking powder, cinnamon, nutmeg, and salt. Whisk until combined.
Combine the wet and dry and mix until JUST combined. The dough may seem a little wet, but the oats will absorb a lot of the moisture. Cover and place in the fridge for 20 minutes. Meanwhile, prepare the creme filling frosting.
Form 6 balls of about 1 and 1/2 tablespoons (30g) of dough (you should get around 38 cookie dough balls) and then slightly flatten the balls. Place very spaced out (these spread a lot) on the baking sheet. Bake for 6-10 minutes (watching carefully) until lightly golden brown at the edges. Be careful to not over bake; these are best slightly under baked. Remove and allow to cool completely.
In a large bowl, beat together the room temperature butter (do not melt!) and 1 cup (95g) powdered sugar. Add in the vanilla and salt. When smooth, add the remaining 1 and 3/4 cup (165g) powdered sugar and beat until smooth. Add the heavy cream as needed. Add up to 1/2 cup additional powdered sugar for a thicker filling.
Once the cookies are COMPLETELY cooled, frost one side of each cookie with the creme filling. Sandwich the two together and enjoy! These are best enjoyed within 1-3 days.