Stir water and sugar in a large pot. Place on back-most burner of your stove. Heat to syrup consistency, on a gentle boil, about 45 minutes. Add vinegar and bring to a boil again. Lastly add mint and continue to boil another 15 minutes. Turn off the heat and allow the syrup to cool overnight. To serve, combine 1-2 tablespoons of syrup (to taste), freshly shredded Persian cucumber, chilled water, and top with ice. Add a tall spoon, so you can eat the cucumber, and a straw. For a high-end presentation, use a long-necked glass. For a more Southern presentation, use a Mason jar and grab a striped straw.