Preheat oven to 400°F. Line a large sheet pan with parchment paper or a silicone liner (very important for these cookies!).
In a large bowl, cream together softened butter, brown sugar, and granulated sugar until light and creamy. Beat in the eggs and vanilla extract.
In another bowl, whisk together flour, oats, baking soda, baking powder, cinnamon, nutmeg, and salt.
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 refrigerate for 20 minutes. Meanwhile, prepare the creme filling frosting.
Form 6 balls of about 1-1/2 tablespoons (30g) of dough (around 38 cookie balls). Slightly flatten the balls. Place dough balls on the baking sheet, allowing plenty of space for spreading. 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 from oven and allow to cool completely.
Creme Filling/Frosting
In a large bowl, beat together the room-temperature butter and 1 cup (95g) powdered sugar. Add vanilla and salt. When smooth, add the remaining 1-3/4 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 3 days.
Notes
Storage: Store leftovers in an airtight container at room temperature for up to 3 days or in the fridge for up to a week.