In a cocktail shaker, combine 2 pear slices, vodka, syrup, juice of 1/2 lime and 1 teaspoon grated ginger, and fill with ice. Shake vigorously and use a teaspoon to taste a little. Add more simple syrup or lime juice to taste. When you are happy with the flavor, strain into a chilled martini glass.
Garnish by threading a thinly sliced round of lime from the remaining half and a chunk of pear from one of the remaining slices onto a wooden pick.
Pear Simple Syrup
Bring sugar and pear juice to a boil in a small saucepan. Simmer gently until the sugar has dissolved, about 2 minutes. Remove from heat and cool completely before using.