Heat the oven to 300 degrees. In a large mixing bowl, whisk the egg white until frothy, then whisk in the brown sugar until combined. Add the almonds and stir until they are evenly coated.
Spread the almonds into a single, evenly spaced layer on a parchment-lined baking sheet. Cook until the almonds are golden brown, 15 to 20 minutes.
While the almonds are toasting, in a small bowl combine the sugar, cinnamon and cayenne pepper, set aside.
When the almonds are done, immediately sprinkle cinnamon sugar mixture over the nuts, using a spatula to toss the hot almonds until evenly coated. Set the almonds aside to cool completely before using. (*This makes a generous 2 cups spiced candied almonds, more than is needed for the remainder of the recipe; the almonds will keep, sealed in an airtight container, at room temperature for up to 2 weeks. You can also store them in the freezer and they will keep for quite awhile.)
In a large bowl add the mixed greens, apple slices, one-half of the spiced candied almonds, one-half of the goat cheese (added in small dollops), the red onion, and chicken. Drizzle desired amount of dressing over salad and gently toss together, sprinkle with remaining candied almonds and goat cheese. Serve immediately.