Brown the pork:In a large saucepan over medium-high heat, warm 1 Tbs. of the olive oil. Working in batches if needed to avoid crowding, add the pork and cook until golden brown on all sides, about 6 minutes. Using a slotted spoon, transfer to a plate.
Simmer the soup: Reduce the heat to medium and warm the remaining 1 Tbs. oil. Add the onion, garlic, chilies and rice and stir to coat with the oil. Add the broth and bring to a boil. Reduce the heat to low, cover and simmer until the rice is tender, about 15 minutes.
Finish the soup:Return the pork to the pan, stir in the cilantro and lime juice, and cook until the pork is cooked through, about 5 minutes. Season with salt and pepper. Ladle into bowls and serve immediately.