Fill a medium saucepan one quarter with water and bring to a simmer
 over medium heat. Place the 64 per cent and 55 per cent dark chocolates and the butter in a stainless steel bowl and set it over the water, stirring until the ingredients are melted together. Remove from the heat and set aside.

Place eggs and granulated sugar in the bowl of a stand mixer fitted with the whisk attachment and process at high speed until light and fluffy, about 8 to 10 minutes. Using a spatula, fold in the espresso and vanilla. Fold the egg mixture into the warm chocolate mixture.

In a small bowl, combine the flour, baking powder, salt, chocolate chips, white chocolate and walnuts. Add to the chocolate-egg mixture and mix by hand until just combined. Refrigerate the dough until firm enough to handle, about 1 hour.

Lightly dust a clean work surface with the icing sugar. Divide the dough into 4 equal parts and, using your hands, roll each piece into a log 12 inches long and about one and a half inches in diameter. Roll each log in the icing sugar to prevent it from sticking. Set the logs on a plate and refrigerate, uncovered, until firm, about 30 minutes.

Preheat the oven to 325°F. Line a baking tray with parchment paper. Using a sharp knife, cut each log into 12 to 14 equal slices and place them, cut side down, on the lined baking tray. Place the first baking tray on a second one so the cookies bake evenly and the bottoms do not burn. Bake for 10 minutes, until the edges of the cookies are just set and the centres are still soft. Do not overbake.

Transfer the cookies to a wire rack to cool slightly, but serve warm. Leftovers will keep in an airtight container at room temperature for 2 to 3 days.