Step 1Heat oven to 325 degrees. Line a rimmed baking sheet with parchment paper.
Step 2In the bowl of a stand mixer, or in a large bowl using a hand mixer, beat the egg whites until they form soft peaks, as if beating a meringue. Slowly beat in the sugar, followed by the allspice, cumin, cayenne, paprika and salt.
Step 3Toss the almonds, hazelnuts, walnuts and pumpkin seeds in the spiced egg white mixture until well-coated. Spread out the nuts on the prepared baking sheet.
Step 4Bake the nuts until they are a nice golden brown, 40 minutes to an hour, opening the oven to stir the nuts every 6 to 8 minutes (the mixture will be thick and messy at first), then more frequently (every 3 to 4 minutes) as they begin to darken. Cool the nuts on the baking sheet, then break up any clumps and toss the nuts with the orange zest. This makes about 5 cups of nuts.