Preheat oven to 350°F and line a baking tray with foil.
In a large bowl, combine the olive oil, orange, lime juice, garlic, oregano, cumin, onion, and pepper.
Remove pork loin from the package and place in a dish.
Pour marinade over pork to fully coat it.
Cover with foil or plastic wrap and refrigerate for at least 2 hours.
Heat 2 tablespoons vegetable oil in a skillet over medium-high heat.
Transfer pork from marinade to skillet.
Strain the onions from the marinade and add to the pan.
Sear pork well until all sides are browned and crispy, about 15 minutes. Remove from heat.
Transfer pork, onion, and pan juices onto the prepared baking tray and wrap in foil.
Place in the oven and braise for 1 – 1 1/2 hours or until pork shreds easily with a fork. Remove pork from the oven and let rest for 10-15 minutes.
Shred the pork using two forks by gently pulling the pork apart using an outward motion.
Serve warm with Cuban style rice and beans and baked maduros.
Garnish with lime.
Serve and enjoy!