Preheat oven to 350 degrees.
Line a baking sheet with parchment paper and set aside.
In a mixing bowl, whisk together the first 8 ingredients (through nutmeg) and set aside.
To the bowl of a stand mixer, add melted butter, oil, and brown sugar and beat until combined.
Add in eggs, pumpkin, and vanilla and beat for about 1 minute.
Add in the flour mixture, a little at a time, beating until just combined after each addition. Batter will look like thick cake batter at this point.
Use a small cookie scoop or Tbsp measuring spoon and scoop batter onto baking sheet, about 2 inches apart.
Bake for 12-14 minutes. Tops of cookies should spring back when touched lightly.
Let cool on baking sheet for a few minutes, then transfer to a cooling rack.
While the cookies are cooling, make the frosting.
In a small saucepan, over MED-LOW heat, melt the butter. Continue heating the butter until it turns a light golden brown color. Set aside and let it cool for 15 minutes.
In a stand mixer, beat the cooled browned butter and softened cream cheese on MED speed, until light and fluffy (about 2 minutes).
Add in maple syrup, cinnamon, nutmeg, salt and ground cloves and mix on LOW until just combined.
Slowly and gradually beat in the powdered sugar.
To one of the cooled cookies, spread about 2 tsp of the frosting, then top with another cookie. Place on a wax paper lined baking sheet and chill in the refrigerator for about 30 minutes.
If desired, sprinkle with powdered sugar just before serving.