In a large pot, heat the olive oil over medium heat. Add the minced garlic and diced onion, sautéing until the onion is translucent, about 5 minutes.
Stir in the smoked paprika and cook for an additional minute, allowing the flavors to meld.
Pour in the vegetable or chicken broth and add the undrained diced tomatoes. Bring the mixture to a simmer.
Add the cooked rice to the pot and stir well. Allow the soup to simmer for 10 minutes to heat through.
Crack the eggs directly into the soup, spacing them evenly. Cover the pot and let the eggs poach in the simmering broth for about 5-7 minutes, or until the whites are set but the yolks remain runny.
Season the soup with salt and pepper to taste. Serve hot, garnished with fresh chopped parsley.