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.
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.
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.