In a small bowl, stir together 2 tablespoons orange juice and cornstarch until smooth. Set aside.
In a medium saucepan over medium-high heat, heat 1 tablespoon oil. Add shallots, ginger, garlic, and red pepper flakes; cook, stirring frequently, until shallots are light golden, about 3 minutes. Add remaining orange juice, broth, and soy sauce. Bring to a boil; boil until reduced to 1 cup, about 6 minutes. Whisk in cornstarch mixture; boil 1 minute. Remove saucepan from heat and set aside.
Place pork slices cut side down on work surface and flatten slightly with the palm of your hand to make medallions. Sprinkle with salt and pepper.
In a 12-inch nonstick skillet over medium-high heat, melt butter with remaining 1 tablespoon oil. Add pork and cook in batches until browned and cooked through, 4 to 5 minutes per side. Transfer pork to a platter.
Add sauce to skillet with drippings; place skillet over medium-high heat. Bring sauce to a boil, stirring to scrape up any brown bits. Stir in juices from pork on platter. Remove skillet from heat and add pork slices to skillet, turning to coat with sauce.