Preheat oven to 300°F and line 2 baking sheets with parchment paper or silicone baking mats.
In a medium mixing bowl, whisk the egg white until frothy. Add the sugar and salt, and whisk to combine. Transfer half of the egg white mixture to a second mixing bowl.
In the first mixing bowl, toss the walnuts and pumpkin pie spice with the egg white mixture. In the second bowl, toss the almonds and berbere spice with the remaining egg white mixture.
Spread out the nuts onto the baking sheets. Bake for 45 minutes, stirring once halfway through. The nuts are ready when they are fragrant and browned. To check for doneness, cut an almond in half. When it is toasty brown all the way to the center, the nuts are ready.
Cool the nuts on their baking sheets until they are at room temperature, about an hour. Store them for up to 2 weeks in a tightly sealed container.