Preheat oven to 375°F. In a medium skillet, cook onion in 2 tsp. oil over medium heat for 3 minutes. Stir in 1 1/2 cups figs and vinegar and cook for 2 minutes. Let cool.
Slice pork loin lengthwise three quarters of the way into meat. Open sections like a book and fill with cooked figs. Fold up pork and secure with kitchen string. Season with 2 tsp. salt and 1/2 tsp. pepper.
Place a roasting pan over medium-high heat. Add remaining 1 Tbsp. oil. Place pork loin in pan and sear on all sides until nicely browned, about 6 minutes. Place pan in oven and cook pork to 150°F on a meat thermometer, 20 to 25 minutes. Transfer roast to a platter; cover with foil.
Drain off all but 1 1/2 tsp. oil from roasting pan. Add shallot and cook over medium heat for 3 minutes, scraping brown bits from bottom of pan. Add port and remaining figs and cook over medium-high heat for 5 minutes. Add chicken broth and cook for 3 minutes. Remove sauce from heat and season with remaining 1/4 tsp. each salt and pepper. Stir in any juices that have accumulated on the platter with pork.
Cut pork into slices 3/4 to 1 inch thick. Top with fig sauce and serve with mashed potatoes and a vegetable of your choice.