Using a pencil, draw ten 2-in. ovals on three sheets of parchment paper. Place paper, pencil mark side down, on baking sheets; chill until ready to use.
In a large heavy saucepan, combine the sugar, water, corn syrup and cream of tartar. Cook and stir over medium heat until sugar is dissolved. Bring to a boil. Cook, without stirring, until a candy thermometer reads 325° or mixture is a golden amber color.
Remove from the heat; stir in oil (keep face away from mixture as oil is very strong). Immediately ladle mixture over ovals; press a cinnamon stick into each. Cool completely. Store in an airtight container for up to 1 month.