In a separate bowl, whisk together the all-purpose flour, cocoa powder, pumpkin pie spice, baking powder, baking soda, and salt.
Add the softened butter and granulated sugar to a mixing bowl and mix until creamy.
Add the egg and egg yolk, then mix until well combined.
Add the vanilla extract and mix until smooth.
Add the pumpkin puree and mix until evenly incorporated.
Add the dry ingredients to the wet mixture.
Add the milk and mix until combined.
Add the melted chocolate to the batter and whisk until smooth and evenly combined.
Pour the batter into the prepared cupcake liners, dividing it evenly.
Bake at 350°F (175°C) for 18–22 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cupcakes from the oven and allow them to cool completely.
For the frosting, beat the softened butter and cream cheese until smooth and creamy, then add the powdered sugar, pumpkin pie spice, and pumpkin puree and beat until smooth and fluffy. Transfer the frosting to a piping bag fitted with a star tip.
Pipe the pumpkin cream cheese frosting onto the cooled cupcakes.
Sprinkle chocolate chips over the frosted cupcakes, then serve and enjoy!