Make the ginger syrup: Combine sliced ginger, sugar, and 1 cup water in a small saucepan and bring to a boil over medium-high heat for five minutes until all sugar is dissolved. Remove from heat and allow to cool to room temperature for 30 minutes. Strain out ginger solids and discard, reserving syrup in an airtight container.
Divide chopped pear between two 12 oz. tall collins glasses; muddle in each glass with a wooden muddler. Pour 2 oz. vodka over the pears in each glass, and fill with ice. Add ½ oz. ginger syrup and ½ oz. lemon juice to each glass, stir to combine, and finish to top of glass with ginger ale.