Prepare Brown Butter: Melt the unsalted butter in a medium saucepan over medium heat, stirring until golden brown, about 5-7 minutes. Let cool slightly.

Blot Pumpkin: Place pumpkin puree on paper towels to absorb moisture for 10-15 minutes, then pat dry.

Mix Dry Ingredients: Whisk flour, spice blend, baking soda, and salt in a bowl.

Cream Butter and Sugars: Beat cooled brown butter with light brown and granulated sugars for 2-3 minutes until fluffy.

Combine Wet Ingredients: Add egg yolk, pumpkin puree, and vanilla to the butter mixture and mix until smooth.

Incorporate Dry Mix and Oats: Gradually mix in dry ingredients and fold in oats until evenly distributed.

Chill Dough: Refrigerate dough, covered, for at least 1 hour.

Bake Cookies: Preheat oven to 350°F (175°C). Scoop dough onto lined baking sheets and bake for 10-12 minutes.

Cool Cookies: Let cookies cool on the baking sheet for 5 minutes before transferring to a wire rack.

Frost: Mix browned butter with cream cheese and powdered sugar, adding milk to reach spreadable consistency. Frost half the cookies and sandwich together.