Prepare a simple syrup by combining the water, sugar, and sweetened condensed milk in a saucepan and heat over medium heat until the sugar is melted.

Remove the saucepan from the heat and let the syrup cool.

When syrup is cooled, muddle mint in the bottom of pitcher.

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Add the sparkling water, cooled simple syrup, and fresh lime juice, as well as half of the cucumber slices, and rum (if adding).

Stir. Add desired amount of ice.

Serve with a cucumber and mint garnish.