1. Preheat oven to 375°.
2. Rub pork with thyme, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Place pork on a broiler pan coated with cooking spray. Bake at 375° for 1 hour or until a thermometer registers 155° (slightly pink). Let stand 10 minutes before slicing.
3. While pork stands, combine 1/4 cup figs and apple juice in a small saucepan; bring to a boil. Cover, reduce heat, and simmer 5 minutes. Remove from heat; cool slightly.
4. Place fig mixture, broth, and next 3 ingredients in a food processor, and process until smooth. Spoon mixture into a small bowl. Stir in shallots, remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, and remaining 1/4 cup figs. Serve immediately with pork.