Step 1: Prepare Brown Butter: In a light-colored saucepan, melt 1 cup of unsalted butter over medium heat, stirring constantly for about 5–6 minutes until it turns a deep golden brown and emits a nutty aroma. Pour the brown butter into a bowl and allow it to cool in the fridge for 30 minutes.

Step 2: Mix Cookie Dough: Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper. In a mixing bowl, cream together 1/2 cup of the prepared brown butter and 1 cup of dark brown sugar until fluffy and light. Add either 1/4 cup pumpkin puree or a large egg, alongside 1 tsp of vanilla extract, and mix until smooth.

Step 3: Incorporate Dry Ingredients: Slowly fold in 1 1/4 cups of all-purpose flour, 3/4 cup of old-fashioned oats, 1 tsp of baking soda, 1/2 tsp of ground cinnamon, and 1/2 tsp of fine salt into the wet mixture. Mix gently until just combined.

Step 4: Bake Cookies: Using a tablespoon scoop, drop 32 balls of dough onto the prepared baking sheets, spacing them about 2 inches apart. Bake for 8–9 minutes, until the edges are set but the centers remain soft. Allow them to cool on a wire rack.

Step 5: Prepare Frosting: In a bowl, beat together the remaining 1/2 cup of brown butter and 1/4 cup of cream cheese until smooth. Gradually add in 1 cup of powdered sugar, 1 tsp of vanilla extract, and 1/4 tsp of fine salt, mixing until fully blended.

Step 6: Assemble Cookies: Once the cookies have cooled, spread the frosting onto half of the cookies and sandwich with another cookie.