Adjust rack in lower third of oven and preheat oven to 350 degrees F.
Line a 10 by 15-inch jellyroll pan with aluminum foil, leaving a 2-inch overhang at each short end.
Mix the ground nuts with the cocoa, espresso, spices, salt and pepper in a small bowl. In a large bowl, whisk the eggs and sugar to combine. Rest the bowl in a hot water bath (hot to the touch, about 120 degrees) and whisk until slightly above body temperature (100 degrees F). Remove bowl from the water bath and using a heavy-duty mixer, whip mixture, preferably with a whisk attachment at medium speed until it is light ivory in color and very fluffy, about 6 minutes. Add the vanilla extract in the final minutes of whipping. Fold in half of the ground pecan mixture until incorporated and then fold in remaining pecan mixture. Pour the batter into the prepared pan and spread it evenly. Bake 8 to 11 minutes or until the cake is set on top and springs back when lightly pressed in the center.
Remove pan from the oven, run a knife around the edges to loosen the cake from the sides of the pan. Lift the cake by the foil overhang to remove from pan and transfer to a wire rack to cool. Cover the cake with a sheet of aluminum foil, folding the foil in a tent-like fashion so that it does not stick to the cake but keeps the moisture in while the cake cools. Cool for 30 to 60 minutes. Lift the cake in its foil off the wire rack to the work surface.
Roll the cake until it forms the shape of a log. Wrap securely in aluminum foil and freeze. About 30 minutes before serving, remove cake from freezer to a serving plate; discard foil. Sprinkle top of roll with powdered sugar. Using a serrated knife, cut slices, diagonally. Center each portion onto individual powdered sugar over slices.