From Serious Eats
Ingredients
2 bananas, peeled and sliced
1 1/2 cups light rum
1/2 cup water
1/2 cup turbinado sugar
Method:
Place the banana slices in a sealable glass jar, then add the rum. Seal and shake.
Let mixture steep for 3 days at room temperature away from direct sunlight.
Strain out the fruit, then filter mixture through through two layers of cheesecloth, pressing down to extract liquid.
Repeat the straining to get any debris that made it through the initial pass.
Heat water and sugar in a pot on medium heat until it boils and forms a syrup, 7 to 10 minutes. Let syrup cool.
Combine syrup with banana infusion. Seal in bottle or jar, then shake to mix. Let rest for a minimum of one day.
Store in the refrigerator for up to two months.