Toast walnut kernels in a pan or oven, let cool and chop coarsely.
Add milk, sugar and cocoa powder to a small, thick-bottomed saucepan and stir thoroughly.
Place the saucepan on the stove and bring the cocoa mixture to a boil while stirring.
Cook the cocoa mixture, stirring, for about 1 minute and remove from heat.
Immediately add butter cut into pieces to the hot cocoa mixture and stir until butter is melted.
Crumble half of butter cookies finely and the other half coarsely.
Add the coarsely and finely crumbled butter cookies and the chopped walnuts to the cocoa mixture and mix to make a sticky chocolate mixture.
Spread a double layer of plastic wrap on the work surface, spread the chocolate mixture lengthwise on one side of the wrap, form it into a "sausage" about Ø 5 cm thick and wrap it tightly with the plastic wrap, tying the ends tightly.
Place the chocolate sausage in the refrigerator for about 3 hours or in the freezer for about 1 hour, until it is firm to the touch, and then remove the cling film.
Dust the chocolate salami with powdered sugar and cut into slices.