Peel and chop bananas into 1-inch pieces.
In a medium saucepan, mix bananas, lime juice, both sugars, water, vanilla, cinnamon, and rum (if using).
Bring to a boil over medium-high heat, stirring to dissolve sugars. Reduce heat to low and simmer for 20–25 minutes, stirring occasionally. The mixture will thicken as water evaporates.
To check readiness, place a spoonful on a chilled plate. If it wrinkles when pushed, it’s set. If not, simmer a few more minutes.
Let cool slightly. Transfer to a jar. Store in the fridge for up to 2 weeks.
