Preheat an oven to 375°F Line a rimmed baking sheet with aluminum foil and lightly butter the foil.

In a small bowl, combine the sugar, cinnamon, cardamom, cloves, salt and pepper. In another bowl, whisk the egg white until frothy. Add the sugar mixture and whisk to blend, then whisk in the orange zest. Add the walnuts and stir until thoroughly coated. Spread the walnuts on the prepared baking sheet in an even layer.

Bake the walnuts, stirring every 10 minutes to loosen them, until golden, about 30 minutes. Transfer the walnuts to a bowl and let cool. Store in an airtight container for up to 3 weeks.