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Make the simple syrup: combine all ingredients for the simple syrup in a sauce pan on low heat. Stir until sugar has dissolved.
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Leave on low (all the way down low) heat for 20 minutes. Let cool, strain to remove the ginger pieces and pour into a jar and refrigerate.
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Make the martini: to a shaker, add crushed ice and all ingredients for the martini. Shake, shake, shake.
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Pour into a chilled martini glass and garnish with pear cubes skewered onto a martini pick!