If you have a food processor, combine the walnuts, dates, 1 cup of coconut, brown sugar, and 1 egg. Blend until a fine paste forms, about 3 to 5 minutes. Skip to step 4.
If not using a food processor, finely chop the walnuts and dates using a food chopper or blender until they reach a paste-like consistency.
Transfer the mixture to a large bowl. Stir in 1 cup of coconut, brown sugar, and 1 egg until evenly combined.
Divide the dough into four equal portions. With damp hands, roll each portion into a 15-inch rope, about 1 inch thick. Place the ropes on a tray, cover, and refrigerate for at least 1 hour.
Preheat the oven to 350°F.
In a small bowl, whisk the remaining egg.
Once chilled, cut each rope into 12 equal pieces by dividing it into thirds, then cutting each section in half twice.
Dip each piece into the beaten egg, then roll in the remaining 1 cup of coconut. Arrange them evenly on a parchment-lined baking sheet.
Bake for 15 minutes. Since these cookies do not spread, all four dozen can be baked together on a full-sized baking sheet. Let them cool completely before serving.