Pre-heat oven to 350 degrees and line two baking sheets with parchment paper.
In a large bowl, whisk together flour, cinnamon, nutmeg, baking powder, baking soda, and salt.
In the bowl of a stand mixer or in a large bowl with a hand mixer, beat together the butter and brown sugar on a medium-high speed until creamy, 2-3 minutes. Add the pumpkin puree in and beat until combined.
Add eggs and vanilla and beat until light and fluffy. Gradually add in the flour and mix until just blended, taking care not to over-mix.
Using a large cookie scoop (about 2 Tbsp), scoop batter onto prepared baking sheets, a couple inches apart. Slightly flatten cookies with back of scoop. Press toasted walnuts onto half of the cookies.
Bake for 14-16 minutes, until the cookies spring back when lightly pressed. Cool on pan for a couple minutes before moving to baking racks to cool completely.
Scoop about 1 Tbsp marshmallow filling onto the non-walnut side of one of the pumpkin cookies and then top with another cookie. Press down a little so the filling spreads to the edge of the sandwich.
Individually wrap each whoopie pie in plastic wrap and keep in the fridge for about an hour before enjoying.