Preheat the oven to 350F and line a 12 cupcake tin with paper liners.
In a large mixing bowl, combine the flour, brown sugar, baking powder, instant espresso, and pumpkin pie spice.
In another bowl, combine the vegetable oil, pumpkin puree, whole milk, ¼ cup coffee, eggs, and vanilla.
Add the wet ingredients to the dry and mix just until they are combined-- be sure not to overmix!
Divide the batter between the tins, filling each one ¾ of the way full.
Bake the cupcakes for 14-16 minutes, or until a toothpick inserted into the center comes out clean.
While the cupcakes are warm, remove them from the pan and allow to cool on a wire rack and poke the top a few times with a fork. Drizzle over the remaining ¼ cup coffee (I added about 1 teaspoon to the top of each cupcake).
Set the cupcakes aside to cool completely before frosting.