Place a saucepan over medium-high heat; add water, brown sugar, and white sugar. Whisk until sugar dissolves, 3 to 5 minutes. Whisk cinnamon into sugar mixture until incorporated. Continue whisking mixture until just before boiling and syrup-consistency, 3 to 5 more minutes. Remove saucepan from heat and stir in vanilla extract.

Cool syrup completely, at least 1 hour. Pour syrup into a glass container and seal; store in refrigerator for up to 10 days.