For the vanilla ginger syrup: Add the sugar to 1/2 cup water in a small saucepan. Scrape the seeds out of the vanilla bean and add them and the whole pod to the saucepan along with the ginger. Bring the mixture to a boil, whisking until the sugar dissolves, then simmer for 1 to 2 minutes. Remove from the heat and set aside to cool to room temperature. If you're making this ahead of time, store it in the fridge with the vanilla bean pod and ginger still in the syrup. If you're using it as soon as it cools, remove the ginger and the pod. (This will make about 1/2 cup of syrup; keep it stored in the fridge for a week or so.)
For the cocktail: Fill a copper mug with ice. Stir the vodka, pear cider and 1 ounce vanilla ginger syrup in the mug. Top it off with ginger beer, drop in a few pear slices and serve!