In a large, heavy-bottomed skillet, heat about 1-inch of oil to 350 degrees F.
Bring a large pot of water to a boil. Add walnuts and blanch for 30 seconds. Drain and transfer nuts to a medium bowl. While nuts are still hot and slightly wet, add confectioners' sugar and toss to coat nuts. Stir and toss until all the sugar has melted into the nuts; if bits of un-melted sugar remain on the nuts, they will not fry properly.
Stir the nuts again before frying. Using a large slotted spoon, transfer a few nuts to the hot oil, allowing the foam to subside before adding another spoonful. (Otherwise, the oil could foam over and burn you.) Fry in small batches until the nuts are medium brown, about 45 seconds; be careful not to overcook. Scatter on an unlined baking sheet to cool slightly.
In a small bowl, stir together cayenne, cinnamon, a pinch of salt, and pepper.
While the nuts are still warm, transfer them to a bowl and sprinkle evenly with about half of the spice mix. Toss well to distribute the spices and then taste a nut. Add more spice mix, to taste, and toss well after each addition. When cool, pack in an airtight jar. They will keep at room temperature for at least 2 weeks.