In a stand mixer fitted with the paddle attachment, beat together the butter, brown sugar and granulated sugar until light and fluffy, about 2 minutes.
Scrape down the sides of the bowl and add the egg and vanilla extract and beat until well combined.
Add the flour, espresso powder, baking soda, baking powder, and salt into the bowl and beat on low speed until just combined and no streaks of flour remain.
Use a 1.5 ounce cookie scoop to scoop out equal amounts of dough and place on the prepared baking sheet, spacing the dough 2 inches apart.
Bake until the cookies have puffed up and are set and firm around the edges but still slightly gooey in the middle, 13 to 14 minutes. Transfer the cookies to a cooling rack to cool completely.
Once the cookies have cooled, make the frosting. In a stand mixer fitted with the paddle attachment beat the heavy cream and powdered sugar together until combined, about 20 seconds. Add the mascarpone, vanilla extract and salt and beat only until combined, about 30 seconds. Transfer the frosting to a piping bag fitted with a round tip and pipe spirals of frosting onto each cooled cookie.
When ready to serve, dust with cocoa powder and devour! Store the cookies covered in the fridge for up to 5 days!