Preheat oven to 350 degrees. Spread almonds on a rimmed baking sheet; toast until fragrant, about 10 minutes. In a large bowl, combine sugar, salt, and cayenne pepper.
In a large skillet over medium heat, cook honey and water with olive oil, stirring, until combined, 1 minute. Add almonds; toss to coat.
Transfer nuts to sugar mixture (do not scrape extra glaze into bowl); toss to coat. Cool in a single layer.
These nuts will keep for up to 2 weeks; let cook completely, then store in an airtight container.