Preheat the oven to 325 degrees F. Cook the bacon over medium heat in a large skillet until brown and crisp, 8 to 9 minutes. Remove the bacon using a slotted spoon and drain on paper towels. Pour 1/4 cup of the bacon fat on a heavy rimmed baking sheet and spread evenly.
Beat the egg white and salt until just foamy using a whisk in a medium bowl. Gradually add the sugar and beat until just blended. Add the almonds, walnuts and cayenne pepper. Toss until the nuts are coated.
Spread the nut mixture in a single layer on the baking sheet. Bake until the nuts are crisp and brown, about 35 minutes, turning and stirring the nut mixture with a metal spatula every 10 to 15 minutes. Cool for 2 hours.
Transfer the nut mixture to a bowl; add the bacon pieces and toss to blend. This recipe can be prepared 1 day ahead and stored in an airtight container in the refrigerator.