Prepare the Banana Simple Syrup: Combine banana slices, granulated sugar, and water in a small saucepan over medium-high. Bring to a simmer, stirring often and gently mashing banana pieces slightly, until sugar dissolves, about 5 minutes. Remove from heat, and let cool to room temperature, about 30 minutes. Pour mixture through a wire-mesh strainer, stirring to remove as much syrup from solids as possible without pressing on solids. Discard solids. Refrigerate syrup in an airtight container up to 1 week.
Prepare the Daiquiri: Process rum, orange juice, Banana Simple Syrup, lime juice, bananas, Cointreau, and ice in a blender on high until mixture is smooth and icy, about 30 seconds. Pour into 2 frozen 16-ounce glasses, and serve immediately.
Excerpted from Beach Cocktails by the Editors of Coastal Living. © 2017 Oxmoor House.