Step 2: In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugars at medium low speed until combined. Increase speed to medium and continue to beat until pale and fluffy, about 3 minutes, stopping halfway to scrape the sides of the bowl.
Step 7: Warm the milk in the microwave for 10 to 15 seconds. Add in the espresso powder and stir until it is fully dissolved. In a medium bowl, sift together the powdered sugar, pumpkin spice, and espresso powder. Add in the vanilla extract and espresso milk and whisk to combine.