In a stand mixer fitted with the paddle attachment, cream the butter, brown sugar, vanilla, and espresso powder on medium speed until just uniform, about 1 minute. Add the flour and salt and mix on medium- low speed until it just comes together. Stir in the walnuts.
Form the dough into a 2-inch / 5cm thick log. Wrap in plastic and refrigerate for at least an hour. You can do this step a couple of days in advance of baking or freeze for 1 month.
Preheat the oven to 325°F / 165°C. Line baking sheets with parchment paper.
Cut the log into slices 1/4 inch / 6mm thick and arrange the cookies on the prepared baking sheets. They won’t spread much but give them a little room just in case.
Bake, one sheet at a time, in the middle of the oven for 12 to 14 minutes, until golden on the bottom. Cool the cookies until firm on the baking sheet and then move to a cooling rack.