In a medium saucepan over medium heat, combine shredded cucumber and water. Bring to a simmer and cook for 15 minutes, or until water has reduced by half.
Strain through a fine-mesh strainer over a bowl and discard the solids. Add sugar to the hot liquid. Stir until sugar has dissolved. Let cool completely.
Transfer to a glass jar and seal tightly with a lid. Store in the refrigerator for up to 1 month.
Cucumber Margarita
Pour some coarse salt on a plate. Rub a lime wedge around the edge of a glass. Roll the rim of the glass in the salt to coat the rim.
In a cocktail shaker filled with ice, add tequila, cucumber syrup and lime juice. Shake well.
Notes
What cucumber to use? Any cucumber would work. I used 3 cocktail cucumbers, which is about the same as 1 large cucumber. Measure out the grated cucumber in cups for best results.To make a cucumber ribbon: Slice a thin strip of cucumber down the long side. (I use a vegetable peeler.) Then fold it gently back and forth, about 1½ inches wide. Pierce with a cocktail pick.Non-alcoholic cucumber margarita: If you prefer a non-alcoholic margarita, use a zero-proof spirit in place of the tequila.