In a large skillet, heat 2 tablespoons olive oil over medium heat. Add the garlic and cook, stirring, for 2 minutes. Stir in the rice for 1 minute. Pour in the chicken broth and bring to a boil. Lower the heat and simmer, covered, for 8 minutes.
Stir in the tomatoes, cover and simmer until most of the liquid is absorbed, about 10 minutes. Stir in the chorizo and peas, cover and cook for 5 minutes more.
In a large nonstick skillet, heat the remaining 2 tablespoons olive oil. Fry the eggs to desired doneness. Divide the rice among 4 bowls, top each with a fried egg and sprinkle with parsley.