Brazilian Limeade

Ingredients
5 cups cold water, divided
1/2 cup coconut milk
1/2 cup granulated sugar
1 large overripe banana, peeled (peel should be speckled, not too overripe)
1/4 cup fresh lime juice
Zest of 3 limes
1/2 tsp coconut extract
Directions
Combine 4 cups cold water (if your blender fits 5 cups well enough then you can add all 5 at this point), coconut milk, sugar, banana, lime juice, lime zest and coconut extract in a blender. Cover with lid and blend on low speed for one minute. Pour mixture through a fine mesh strainer into a pitcher, then using a rubber spatula press and rub lime zest back and forth against strainer to release oils from the zest into pitcher. Pour in remaining 1 cup cold water and stir. Serve over ice. Store in refrigerator and stir each time before serving.