Sprinkle pork with salt and pepper. Heat 1 tablespoon oil in heavy large skillet over medium-high heat. Add 4 pork slices and saute until brown, about 2 minutes per side. Transfer pork to baking sheet. Add remaining 1/2 tablespoon oil to skillet. Repeat with remaining 4 pork slices. Transfer pork to oven to keep warm.
Melt 1 tablespoon butter in same skillet over medium-high heat. Add shallots and sauté until tender, about 2 minutes. Add 2 tablespoons balsamic vinegar. Simmer about 1 minute. Add chicken broth. Simmer until mixture is reduced by about half, about 4 minutes. Add figs and whipping cream. Simmer until sauce thickens slightly, about 4 minutes. Add remaining 1 tablespoon vinegar and any accumulated juices from pork. Simmer until sauce thickens enough to coat spoon. Season sauce to taste with salt and pepper.
Arrange pork on plates. Spoon sauce over. Sprinkle with parsley and serve.