In a small bowl, melt the butter and whisk in the espresso powder. Transfer to the fridge and cool for about 10 minutes.
In another bowl whisk together the flour, cornstarch, baking powder, baking soda, and salt until well combined.
In a large mixing bowl, whisk in the cooled espresso butter with the granulated sugar until well combined. Whisk in the egg and vanilla extract until smooth and well combined.
Stir the dry ingredients into the wet until just combined, about ½ of the dry ingredients at a time.
Preheat the oven to 375 F (190 C) for about 20-30 minutes before baking the cookies. Line a large baking sheet with parchment paper and allow the dough to rest while the oven preheats for 30 minutes.
Using a medium cookie scoop (2 tablespoons, 30 ml), scoop the cookie dough and place the cookie dough balls onto the lined baking sheet about 3 inches (8 cm) apart.
Bake at 375 F (190 C) for 10 - 12 minutes or until the edges of the cookies are set and the centers are slightly puffed.
Cool the chewy coffee sugar cookies on the baking sheet for 5 minutes, then transfer to a cooling rack to cool completely.
Make the mascarpone frosting while the cookies cool.
On low, whisk the mascarpone cheese until smooth. Then mix in the espresso powder, vanilla extract, and powdered sugar until well combined.
Once all the sugar has been added, mix in the heavy cream slowly on low speed. Increase the mixer speed to medium for about 2 - 3 minutes or until the frosting is light and fluffy.
Top the soft and chewy espresso sugar cookies with 1 - 2 tablespoons (15 - 30 ml) mascarpone frosting. Smooth the frosting across the top in a circular motion and dust with cocoa powder.