Heat the oil in a 10-inch saute pan over high heat and add the seeds. Toast the seeds, moving the pan constantly, until you smell their aroma and hear some of them begin to crackle, 4 to 5 minutes. Transfer to a small mixing bowl and toss with the cayenne, cinnamon, and salt.
Line a half-sheet pan with a silicone baking mat or parchment paper. Coat the bottom of a second half-sheet pan with vegetable oil.
Set a 3-quart saucier inside a large 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 color and reaches 350°F on a digital instant-read thermometer, about 25 minutes.
Remove from the heat and stir in the pumpkin seed mixture. This will greatly reduce the temperature of the sugar, so work quickly. As soon as the seeds are thoroughly incorporated, pour the mixture onto the lined half-sheet pan. Using an oiled spatula, spread it thinly, working quickly before it hardens. Top with the oiled half-sheet pan and press into a single layer. Cool completely, about 30 minutes, then break into pieces. Store in an airtight container for up to 2 weeks.