1 1/2 cups granulated sugar
3/4 cup water
1 teaspoon vanilla extract
2 ripe bananas, peeled and mashed
3 cups vodka
1. Make a simple syrup by bringing sugar and water to a boil over medium-high heat, stirring constantly to prevent scorching. When clear, remove from heat and add vanilla. Let stand until just warm. Place mashed banana in clean 1-quart, wide-mouthed jar. Add syrup and vodka. Cover and let stand in a cool, dark place for 3 to 4 days, stirring or shaking once or twice a day to prevent clumping of fruit.
2. Use a fine-mesh strainer to strain out solids. Discard. The liqueur will still be cloudy. Cover and let stand undisturbed until it clears. Rack into a clean container. Cover and age for 1 month. If more sediment settles to the bottom, rack again before serving.
Makes 1 quart.
From Classic Liqueurs, by Cheryl Long and Heather Kibbey:
* 1 large, just-ripe banana, peeled
* 1 fifth vodka or light rum
* 1 1/4 cups granulated sugar
* 1/2 cup water
* 2" piece of vanilla bean
Mash banana. Add banana to vodka. Using wooden spoon, submerge banana mash (exposure to air will brown the banana). Steep 2 weeks. Strain, filter, add syrup. Slit open vanilla bean, add to mix. Age 1 month, remove bean. Strain and filter again as necessary. Age another month.
These are just from searches, never tried them, so can't vouch for them at all. If you try one, let us know, I would like something good along these lines.