To make the muffins:

1. Preheat the oven to 425 degrees, and line a 12 cavity muffin pan with paper liners. Sift the flour, espresso powder, baking soda, baking powder, salt and pumpkin pie spice together in a medium mixing bowl and set aside.
2. In another, larger mixing bowl, cream the butter and sugar together on medium speed until light and fluffy, about 3 minutes. Add the eggs one at a time, scraping down the bowl after each one.
3. Add the pumpkin puree and vanilla extract, and beat on low speed just until combined evenly.
4. Alternate adding the flour/spice mixture and milk, beginning and ending with the flour. Add 1/3 of the flour mixture and beat on low speed until there are no flour streaks remaining. Follow up with half of the milk and blend on low speed again just until combined. Repeat with another flour addition, the remaining milk, and then the remaining flour mixture.
5. Use a spatula to gently fold in all but a few tablespoons of the chopped chocolate, reserving some for sprinkling on top of the muffins before baking.
6. Divide the batter evenly among all 12 muffin cavities, filling each one nearly to the top. Sprinkle with the reserved chopped chocolate and bake for 10 minutes at 425. After 10 minutes, reduce the oven temperature to 350 degrees and continue to bake for another 15 minutes. The tops of the muffins should spring back slightly when you press them with your finger.
7. Allow the muffins to cool completely before glazing.

To make the glaze:

1. Combine the espresso powder and hot water in a small bowl or dish and stir to dissolve the powder. In a slightly larger bowl, combine the remaining glaze ingredients and add the espresso powder liquid. Whisk everything together until smooth and pourable, adding more powdered sugar or milk as needed.
2. Drizzle the cooled muffins with coffee glaze as desired.