Crush mint leaves in a shaker filled with ice. Pour vodka, simple syrup, Cointreau, lime juice andpeel, and bitters over the crushed mint. Shake vigorously until shaker is frosted.
Place dry vermouth in a chilled martini glass; swirl the vermouth in the glass and then pour it out. Strain contents of shaker into glass. Cocktail should be icy, with bits of mint and lime. Garnish with mint sprig.
To make simple syrup:
Put 1 cup of water in a small sauce pan. Add 2 cups of sugar. Heat to a boil while stirring. Reduce heat and continue to stir until the sugar dissolves. Cool to room temperature. Pour into a clean container, seal and store in the refrigerator.