Heat a large drizzle of olive oil in a large pan over med-hi heat. Pat chicken dry with paper towel and season with salt/pepper. Cook in pan until no longer pink in center (5-7 minutes per side). Remove and set aside to rest.
Lower heat to medium. Add shallots, rosemary, and a large drizzle of olive oil. Cook, tossing until softened 2-3 minutes. Stir in vinegar and fig jam. Simmer until syrupy, about 1 minute. Stir in stock. Let reduce until thick and saucy, about 3 minutes. Remove from heat. Stir in 2 Tbsp of butter. Season with salt/ pepper.