Heat olive oil in a large pot over medium heat. Add diced onion and cook until it softens and begins to caramelize, about 6–8 minutes.
Stir in drained diced green chiles and cook for 1–2 minutes.
Add grated garlic, sazon, cumin, and salt. Cook for 1 minute.
Add rinsed rice and stir to coat. Toast for 3-4 minutes.
Pour in chicken broth and bring to a boil.
Once the liquid starts to evaporate and the rice begins to show on the surface, give it one good stir.
Reduce heat to simmer, cover, and cook for 20 minutes until rice is fully tender.
Stir in the black beans and cover again for 3–5 minutes.
Add chopped cilantro and lime juice. Stir and adjust salt if needed.
Serve warm.