Preheat your oven to 350°F (175°C). Line muffin tins with cupcake liners.

In a medium bowl, whisk together the flour, espresso powder, baking soda, baking powder, pumpkin pie spice, and salt. Set aside.

In the bowl of a stand mixer with the paddle attachment, blend together the pumpkin puree, granulated sugar, brown sugar, and vegetable oil until well combined.

Add the eggs one at a time, beating well after each addition.

With the mixer on low speed, gradually add the dry ingredient mixture to the wet ingredients in two additions, mixing just until incorporated. Do not overmix.

Fill the cupcake liners about ¾ full with batter. Bake for 20-22 minutes, or until a toothpick inserted into the center comes out clean. Let the cupcakes cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.

In a stand mixer with the paddle attachment, cream the softened butter on medium speed until smooth and creamy.

With the mixer on low speed, slowly add the confectioners' sugar, one cup at a time, mixing until each addition is incorporated.

Mix in the espresso powder and vanilla extract.

Add the milk, starting with 2 tablespoons. Increase the mixer speed to medium-high and beat for 5-8 minutes, or until the frosting is light and fluffy. If the frosting is too thick, add more milk, 1 teaspoon at a time, until your desired consistency is reached. If it's too thin, add a little more confectioners' sugar.

Once the cupcakes have cooled completely, pipe or spread the espresso buttercream frosting on top.