Papaya-Lime Hawaiian Shaved Ice

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1. 1Step 1: To make the syrup, in a bowl, combine the papaya, lime zest and juice, and 1 cup (8 oz./250 g) of the sugar. Toss to combine and let stand at room temperature for 1 hour.
2. 2Step 2: Transfer the content of the bowl to a blender and add 1 cup (8 fl. oz./250 ml) water and the remaining 1 cup (8 oz./250 g) sugar. Blend on high speed until smooth, about 1 minute.
3. 3Step 3: Pour the papaya mixture through a fine-mesh sieve into a bowl. Stir in the Key lime juice.
4. 4Step 4: To serve, use a Hawaiian ice shaver to make enough shaved ice to fill 8 short tumblers or paper cones. Fill the tumblers with the shaved ice.
5. 5Step 5: Divide the syrup evenly among the tumblers, pouring it evenly over the shaved ice.
6. 6Step 6: Sprinkle the finely diced papaya and coconut on top of the shaved ice, dividing them evenly. Garnish each serving with a lime slice, if desired, and serve immediately.