First - Ginger-infuse the cider: Peel and chop the ginger. Bring apple cider to a boil in a nonaluminum pot. Add several slices of cut and peeled ginger when cider boils. Turn heat off and steep for 30 minutes. Puree this mixture in a blender and strain through cheesecloth. Refrigerate until ready to use.
Second - Make the ginger toddy: Heat the ginger-infused cider, but do not boil. Add bourbon. Stir in honey. Pour into a coffee mug. Garnish with lemon and ginger slice (or use crystallized ginger).