To make the banana Simple Syrup:
Heat the water until boiling, reduce heat to low. Add banana slices & sugar; mix until the sugar dissolves while mashing the bananas a little.
Remove from heat & let cool to room temperature. Strain into a storage container, mashing the pulp to get as much liquid as possible -but avoding getting fine material that'll make the syrup cloudy.
Stores in the refrigerator for about a week.
To make the Daiquiris:
Add the rum, orange juice, Banana Simple Syrup, lime juice, peeled bananas, Cointreau, and ice to a blender. Blend thoroughly until smooth.
Pour into two 16 oz glasses. Garnish with a couple slices of banana.