In a large mixing bowl, cream together the light brown sugar, cane sugar, and melted butter. Add in the vanilla bean paste and whisk until combined.
To the creamed sugar and butter, pour in the cold espresso, egg, and egg yolk. Whisk again until fully combined.
Once the wet ingredients are mixed, gently pour in the all purpose flour, baking soda, and espresso powder.
Switch to a spatula and fold gently until the flour and espresso powder and well combined.
Line a baking sheet with parchment paper, then using a large cookie scoop, scoop the cookie dough batter into balls, then place on the baking sheet.
Repeat until all the batter is formed into cookie balls, then chill for an hour in the fridge.
About five minutes before the chill time is up, preheat the oven to 350º, remove the cookies from the fridge, and bake the cookies in batches of 6, evenly spaced. Bake for 11 minutes, then let cool and transfer to a wire rack to finish cooling for 30 minutes.
While the cookies cool, whisk together the mascarpone, half and half, powdered sugar, and espresso. Whisk until very very smooth and there are no lumps.
After the cookies are completely cooled (approximately 15 minutes), use a spoon and spread in a circular motion on the top of the cookie in an even layer. Dust with some espresso powder and serve.
Notes
Use a Scale - In my years of learning from trials and recipe development, I've come to lean heavily on my kitchen scale. I love my Zwilling scale, but you can always buy another kind. When it comes to baking, having precise measurements helps the texture, taste, structure, and mouthfeel stay consistent every time you bake.