Preheat oven to 350° and prepare baking sheet(s) with parchment paper or silicon baking mat.
In a large bowl, whisk together flour, cocoa powder, baking soda and salt. Set aside.
Melt butter and let cool.
In a separate bowl, combine butter with brown and granulated sugars. Mixing by hand with a whisk until glossy in appearance. About 1 minute. Then incorporate eggs, one at a time. Then add vanilla extract.
In a small bowl, whisk together espresso powder and hot water until dissolved. Add liquid to sugar mixture and combine.
In a stand mixer using the paddle attachment, or in a large bowl using a rubber spatula, combine sugar-espresso mixture with flour mixture. Mix until no flour pockets remain.
Roll dough into 2 tbsp balls. Using your fingers, slightly flatten tops to create a disc shape. Arrange discs on baking sheet 2 inches apart to allow for spreading. Bake for 8 minutes then let cool on baking sheet for 5 minutes before moving to wire rack to cool completely.
While cookies are cooling, melt white chocolate according to package instructions. Drizzle cookies with white chocolate and allow to cool, 5 minutes more.
Store cookies in air tight container for up to a week.