Pour maple syrup into a medium saucepan; add cinnamon. Bring to a boil over medium-high heat. Cook until a candy thermometer registers 240 degrees (soft-ball stage), 10 to 15 minutes. Remove the pan from heat, discard cinnamon stick, and stir in butter until melted.
Immediately transfer mixture to the bowl of an electric mixer fitted with the paddle attachment. Beat, starting on low and increasing to high, until mixture is thick, opaque, and creamy, about 8 minutes. Store in an airtight container, refrigerated, up to 2 weeks.