Preheat the oven to 225F and line a large shallow baking pan with foil.
Combine the egg white and water and beat until foamy. Add the nuts and toss to coat. Pour the mixture into a colander or strainer and let drain 2-3 minutes.
Combine the sugar, cinnamon and allspice in a plastic or paper bag, shaking the bag to combine all the ingredients. Add the walnuts, hold the bag shut and shake vigorously to coat the nuts. Spread the nuts in one layer on the prepared baking sheet – it’s okay if they touch – and bake for 2 hours, stirring every 15-20 minutes. Cool completely, stirring occasionally and breaking them apart if they are stuck together. Don’t worry if they stick to the foil; it is easy to peel them off. Store in a tightly-capped jar.