Combine the sugar, water, and lemon zest in a pot over medium heat. Gently simmer for 2 minutes until the sugar is dissolved, swirling the pot over the heat now and then – do not allow to boil or get dark. Put the jasmine in a mason jar or glass container and pour the sugar syrup on top; steep for 1 to 2 hours to infuse the jasmine flavor into the syrup.
In a martini shaker filled with ice, combine the vodka, Grand Marnier, lemon juice, and 4 tablespoons of the jasmine syrup. Shake until frothy and pour into chilled martini glasses. Float a jasmine flower in each glass for great presentation.
1 cup sugar
1 cup water
2 strips orange zest
1 handful pesticide-free jasmine flowers, plus more for garnish