In a small saucepan, combine sugar and water. Bring to a boil over medium/high heat until the sugar has dissolved and the mixture takes on a slightly syrupy texture, about 5-6 minutes. Remove from heat and allow to cool slightly. Set aside.
Mash the ripe bananas in a small bowl. To the mashed bananas add the vanilla bean paste and spices. Mix until combined.
To a 24 ounce mason jar, add the cooled simple syrup, the mashed banana mixture, and vodka. Add the cinnamon sticks and seal. Shake to combine the ingredients. Place in a cool dark place and allow mixture to steep for at least two weeks, shaking it once daily.
The longer your mixture steeps, the deeper the flavor. Just something to think about.
Strain the mixture into a strainer lined with a coffee filter or a cheesecloth, pressing on the solids to extract all that deliciously spiced banana flavor. Transfer the banana liqueur to a mason jar or a glass container with a tightfitting lid. Store in the refrigerator until ready to use.
Lasts forever and ever due to the alcohol and sugar content.