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Preheat oven to 250°F. Mix sugar, cinnamon, red pepper and salt in small bowl. Set aside.
Beat egg white and vanilla in medium bowl until foamy. Add walnuts; toss to coat. Add spice mixture; toss to coat nuts evenly. Spread nuts in single layer on greased baking sheet.
Bake 1 hour, stirring nuts after 30 minutes. Cool slightly and break apart. Cool completely and store in airtight container up to 2 weeks.