Add the ingredients to a medium saucepan and simmer until reduced by half or more, about 35 minutes. You will want the consistency to be syrupy with a flavor that's concentrated. Pour into a glass container and chill.
For the Drink
Add the grapefruit juice and mint to a shaker and muddle.
Add ice to the shaker then pour in the vodka, syrup and lime juice.
Shake well and pour into cocktail glass. Garnish with a twist of grapefruit peel and mint.