Make lemon concentrate: In a medium saucepan, bring 2/3 cup sugar, ginger, 5-in. rosemary sprigs, and 2 1/2 cups water to a boil. Reduce heat to a simmer and cook, stirring occasionally, about 10 minutes. Let steep at room temperature 20 minutes. Strain into a medium bowl, discarding rosemary and ginger, and stir in lemon juice.
Pour remaining 2/3 cup sugar onto a plate. Slice 2 thin slices from lemon and quarter the slices. Insert a 1 1/2-in. rosemary sprig through center of each quarter. With a wedge cut from remaining lemon, moisten the rims of 8 cocktail glasses. Twist rims gently in sugar to coat.
Fill a large pitcher half-full with ice cubes. Pour in vodka and lemon concentrate and stir vigorously. Strain into glasses, dividing evenly. Float a rosemary-skewered lemon quarter in each.
Note: Nutritional analysis is per serving.