Heat 1 1/2 teaspoons oil in a Dutch oven over medium-high heat. Brown pork on all sides. Remove from pan.
Heat remaining 1 1/2 teaspoons oil in pan, scraping pan to loosen browned bits. Add rice, onion, garlic, and chiles; sauté 3 minutes or until onion is tender. Add pork, 1 cup water, oregano, broth, and beans; bring to a boil. Cover, reduce heat, and simmer 15 minutes or until rice is tender. Stir in cilantro, juice, salt, and pepper; simmer 2 minutes. Top each serving with cheese, avocado, and chips.