Cookies

1. Preheat oven to 350°F. Line a baking sheet with parchment paper. Set aside.
2. In the bowl of your stand mixer fitted with the paddle attachment, mix together the butter, oil, and both sugars until smooth on medium speed. Beat in the eggs, vanilla, pumpkin pie spice, baking soda, cream of tartar, and salt, and mix for 1 minute, scraping the sides of the bowl as necessary.
3. Turn the mixer to low and add in flour, mixing until combined.
4. Using a large cookie scoop (3 tablespoons), scoop the dough onto the lined baking sheet. Bake for 10-12 minutes until edges just start to golden. Immediately press the cookies gently, using the bottom of a cup, until they are flat in the middle.
5. Allow to cool for 3 minutes on the baking sheet and transfer to a wire rack to finish cooling.

Frosting

1. In a medium saucepan over medium-low heat, melt the butter and bring it to a boil. Constantly swirl the pan and allow the butter to brown. Once it has reached an amber color, remove from the heat and cool completely. Place the pan in the refrigerator and allow the butter to return to a solid state. Once it’s firm, remove the pan from the refrigerator and allow it to come back to room temperature.
2. Place the butter (making sure to scrape up all of the brown bits) in the bowl of your stand mixer fitted with the paddle attachment. Add in the powdered sugar and mix on medium speed until combined. Add in the vanilla and milk and mix until smooth and creamy, scraping the sides of the bowl as necessary.
3. Mix a few drops of the food coloring into the frosting and stir until combined.
4. Spread a tablespoon of frosting onto each cookie and garnish with sprinkles if desired.