Sweet Potato and Ginger Syrup: Combine the sweet potatoes, ginger, water, and salt in a pot. Bring to a boil, then simmer for 20–30 minutes until tender. Reduce to low heat and stir in the brown sugar until dissolved. Cool for 15 minutes, then blend until smooth. Strain through a fine mesh strainer. Refrigerate for up to 2 weeks.
To prepare a cocktail, fill a rocks glass with an ice ball or fresh ice. Add bourbon, sweet potato syrup, lemon juice, and bitters. Stir until chilled and combined. Garnish with rosemary.