Combine the peanuts, cinnamon, cayenne, and salt a small mixing bowl and set aside.
Line a half-sheet pan with a silicone baking mat. Coat the bottom of a second half-sheet pan with vegetable oil.
Set a 3-quart saucier inside a 12-inch cast-iron skillet. Add the sugar and water to the saucepan and cook over high heat, stirring occasionally with a wooden spoon, until it comes to a boil. Stop stirring, cover, and cook for 3 minutes. Uncover, reduce heat to medium, and cook until the sugar is a light amber in color, approximately 25 minutes. The mixture should reach 350ºF.
Remove from the heat and stir in the peanut mixture — this will greatly reduce the temperature of the sugar, so work quickly. Once evenly mixed, pour the mixture onto the lined half-sheet pan. Working quickly, use an oiled spatula to spread the mixture thin. Top with the oiled half-sheet pan and press into a single layer. Cool completely, about 30 minutes, and then break into pieces. Store in an airtight container for up to 2 weeks.