Prep the oven and pans: Preheat your oven to 350°F. Line two baking sheets with parchment paper. This ensures the cookies won't stick and makes for easy cleanup.
Cream the butter and sugars: In the bowl of your stand mixer fitted with the paddle attachment (or in a large bowl using a hand mixer), beat the 3/4 cup room-temperature butter, 3/4 cup brown sugar, and 1/2 cup sugar together on medium speed until light, fluffy, and pale in color. This takes about 2-3 minutes. Listen for the sound as the mixture changes from a coarse scraping to a soft, aerated whisper—that's when you know it's ready.
Add the wet ingredients: Add the 2 eggs one at a time, mixing well after each addition. Scrape down the sides of the bowl. Then, add the 1/2 cup pumpkin puree and mix until completely combined. The mixture might look a little grainy or separated—that's totally fine. At this point you'll smell the sweet, earthy pumpkin coming through.
Incorporate the dry ingredients: With the mixer on low, gradually add the 1 1/2 cups flour, 1 teaspoon baking soda, 1 teaspoon pumpkin pie spice, and 1 teaspoon kosher salt. Mix just until the flour disappears—overmixing at this stage can make the cookies tough.
Stir in the oats: Turn off the mixer and fold in the 3 cups old fashioned oats using a rubber spatula. The batter will become thick and hearty, and you'll see little oat flakes studding the dough. Make sure they are evenly distributed.
Scoop and coat: Using your 1 Tablespoon scoop, portion out rounds of dough. In a small bowl, whisk together the 1/4 cup sugar and 1/4 teaspoon pumpkin pie spice. Roll each dough ball in the sugar-spice mixture to coat evenly, then place it on your prepared baking sheet, spacing them about 2 inches apart. The coating will give the finished cookies a delicate, crystalline crunch.
Flatten slightly: Using the palm of your hand or the bottom of a glass, gently flatten each dough ball just a bit. This ensures they bake into nice, even disks that are perfect for sandwiching.
Bake to perfection: Bake for 7-8 minutes. You'll know they're done when the edges are just starting to turn a light golden brown and the centers look set but still soft and slightly puffed. Your kitchen will fill with the warm, spiced aroma of pumpkin pie and oats. The baking time is short because of the small size.
Cool completely: Let the cookies cool on the baking sheet for exactly 5 minutes. This allows them to firm up enough to be transferred. Then, move them to a wire cooling rack to cool completely. Resist the urge to fill them while they're warm!
Make the maple buttercream: While the cookies cool, make the filling. In the clean bowl of your stand mixer (or using a hand mixer and a smaller bowl), beat together the 1 cup room-temperature butter, 2 Tablespoons real maple syrup, pinch of salt, and 1/2 teaspoon cinnamon. Beat until smooth and combined, breathing in the intoxicating maple scent. Gradually add the 1 1/2 cups powdered sugar, mixing on low speed until it's incorporated, then turn the mixer to high and beat for 2-3 minutes until the buttercream is light, fluffy, and pale.
Assemble: Once the cookies are completely cool, spread a generous layer of maple buttercream onto the flat side of half of the cookies. Top with the remaining cookies to create sandwiches. Give them a gentle press to secure the filling. The soft, chewy cookies against that creamy, maple-sweet center—perfect.