Preheat the oven to 350F. Line a cupcake tin with liners.
In a medium bowl, mix together the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and allspice together. Set aside.
In a mixer, add both sugars and butter together and beat until light and fluffy. Add the eggs and beat well for at least two minutes. Beat in the pumpkin and vanilla for an additional minute.
In a small bowl, whisk together the espresso powder and milk together.
Alternate between adding the flour mixture and the milk mixture into the mixer. Begin and end with the flour. Add the flour in three additions and the milk in two additions.
Bake for about 15 - 18 minutes, or until a toothpick comes out clean.
Remove the cupcakes and allow to cool in the pan for one minute before removing to cool completely on a wire rack.
While the cupcakes are cooling, make the frosting. Beat the cream cheese using a whisk attachment until it is completely smooth. Slowly beat in the heavy cream and continue to beat until it reaches soft peaks. Add in the powdered sugar and vanilla and beat until it just about reaches stiff peaks.
Top the cupcakes with the frosting and top with caramel drizzle.
The cupcakes are best stored in an airtight container in a cool area for 24 hours, or in the refrigerator for up to three days.