Add the granulated sugar, brown sugar, water, cinnamon sticks, and salt to a small saucepan. Stir to combine.
Place the saucepan over medium heat and bring the mixture to a gentle simmer.
Let the syrup simmer for 10 minutes, stirring occasionally.
Remove the saucepan from the heat and remove the cinnamon sticks. Stir in the vanilla extract, and then let the syrup cool to room temperature.
Transfer the syrup to a bottle or airtight container and store in the refrigerator for up to 3 weeks.