Preheat oven to 375 degrees F (190 degrees C), and line baking sheets with parchment paper or silicone mats.
In a large bowl, stir together the butter, brown sugar, salt, and espresso powder until evenly mixed and creamy. Stir in the egg, egg white, and vanilla until smooth.
Sprinkle the flour, cocoa, and baking soda over the mixture, then stir just until flour is incorporated. Gently fold in the chocolate chips and walnuts.
Scoop the dough into approximately 20 balls, spacing them evenly on the baking sheets. Bake for 8-11 minutes, until cookies are slightly puffy and being to crack on the surface. Let rest on the pans for 5 minutes, then transfer cookies to a wire rack to cool. Cookies will keep up to three days if tightly covered at room temperature.