Preheat the oven to 350°F. 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, granulated sugar, brown sugar, and oil.

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

With the mixture on low speed, add the flour mixture in two additions, mixing just until incorporated.

Fill the cupcake liners ¾ full. Bake until the cupcakes are golden, about 20-22 minutes. Let them cool on a wire rack for 10 minutes; then, remove the cupcakes from the pans to cool completely.

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

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

Mix in the espresso powder and vanilla.

Add the milk, starting with 2 tablespoons. Turn the mixer up to medium-high and beat until light and fluffy, approximately 5 to 8 minutes. If the buttercream is too dry, add more milk, 1 teaspoon at a time, until it reaches your desired consistency.

Pipe (or spread) the buttercream on top of the cooled cupcakes.