In a skillet over medium-high heat, warm 1 tablespoon oil. Add pork and sear.
In a bowl, combine ¼ cup oil, 1 cup orange juice, and ¼ cup lemon juice. Set aside.
When meat is browned, reduce heat to medium. Add garlic, cumin, and salt and pepper. Cook for about 30 seconds. Do not burn garlic. Slowly pour in orange juice mixture. Baste meat with a spoon. Continue basting every 15 minutes for 1 hour. When liquid is reduced and thickened, add remaining oil, 1 cup orange juice, and 1⁄4 cup lemon juice. Continue basting every 15 minutes until pork is tender, adding remaining orange and lemon juices as needed when liquid reduces. Serve with black beans and rice, if desired.