Preparing the Mojo Pork: In a bowl, whisk together orange juice, lime juice, minced garlic, olive oil, cumin, oregano, salt, pepper, and red pepper flakes. Place pork roast in a large resealable bag or dish and pour the marinade over it. Marinate in the refrigerator for 2–4 hours (overnight for more flavor). Preheat oven to 375°F (190°C). Heat 2 tbsp olive oil in a large oven-safe skillet or Dutch oven over medium-high heat. Sear pork on all sides until golden brown, about 3–4 minutes per side. Pour any remaining marinade over pork and transfer to oven. Roast for 1 hour–1 hour 15 minutes, or until internal temperature reaches 145°F (63°C). Let rest 10 minutes before slicing.
Preparing the Black Beans: Heat olive oil in a saucepan over medium heat. Sauté onions until translucent, about 3–4 minutes. Add garlic, cumin, and smoked paprika; cook 1 minute until fragrant. Add black beans and chicken broth. Simmer 10–15 minutes until beans are heated and slightly thickened. Season with salt and pepper to taste.
Preparing the Rice: Rinse rice under cold water until water runs clear. In a saucepan, bring 4 cups water to a boil with salt and olive oil. Add rice, reduce heat to low, cover, and simmer 18–20 minutes until tender. Fluff with a fork before serving.