In a small bowl, stir together the cinnamon, cayenne pepper and 1 tablespoon of the sugar; set aside.
In a 4-quart saucepan, combine 1/2 cup plus 2 tablespoons water and the remaining 1 1/2 cups sugar. Stir over medium-high heat until the sugar dissolves and the mixture boils.
Add the almonds and stir constantly over medium-high heat until the water evaporates and the sugar starts to dry and turn gray. (The sugar mixture will start to foam and then start to dry and look like sand. This takes 5 to 6 minutes.) Continue stirring constantly until the sugar starts to melt and caramelize, coating about half of the almonds in a reddish-brown sugar mixture and the rest in a glossy sugar mixture, 2 to 3 minutes.
Sprinkle the cinnamon mixture over the almonds, stirring constantly, and immediately transfer to a baking sheet lined with parchment paper, spreading the almonds to separate. Cool completely, then break apart. Store the almonds in an airtight container for up to 2 weeks.