Mix the brown sugar, smoked paprika, salt, cinnamon and cayenne pepper together in a medium bowl.
Whip the egg whites in another bowl with a whisk until light and frothy. Drop the nuts into the bowl and toss to combine. Remove the nuts, shaking off any excess egg white, and drop them into the bowl with the spice mix. Toss to coat all of the nuts with the spices.
Spray a baking sheet with nonstick cooking spray or line the sheet with a non-stick baking mat. Spread the nuts on the sheet in a single layer and bake in the oven for 15 minutes, stirring once halfway through. Remove the nuts and let them cool on a wire rack. As they cool, they will crisp up. Serve right away or store in an airtight container for one week.