Do ahead: Peel skin from ginger root with the side of a spoon. Finely grate enough ginger to prepare as many drinks as needed.
To make one cocktail drink: Juice lime and pour into martini shaker. Add two pear slices to the martini shaker. Add thumbnail-sized portion of ginger and muddle ingredients together.
Pour syrup from canned pears into shaker. Fill shaker with ice and add vodka. Shake vigorously 10 times and strain into chilled martini glass, making sure to keep solids out of the cocktail.
Nutritional Information Per Serving: Calories 170 (based on 80-proof vodka)
Note: One, 15-ounce can of pear slices in heavy syrup makes 8 drinks.
Note: Higher-proof vodka contributes more calories.
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