Place the rice in a heatproof bowl. Bring the water to a boil and pour it over the rice. Let soak for 40 minutes, then drain; set aside.

Meanwhile, in a sauté pan over medium heat, warm two tablespoons of the vegetable oil. Add one of the onions and sauté until soft, about five minutes. Remove from the heat and let cool.

In a bowl, combine the pork, beef, cooled onion, soaked rice, egg, cumin, oregano, ¾ teaspoon salt and ½ teaspoon pepper. Using your hands, mix well and form into one-inch balls.

In a large soup pot over medium heat, warm remaining two tablespoons vegetable oil. Add remaining onion and sauté until soft, about five minutes. Add garlic, zucchini, carrots, and tomatoes and cook, stirring, until fragrant, about five minutes.

Add the chicken stock, stir well, and bring to a boil. Carefully slip the meatballs into the pot, reduce the heat to low and simmer uncovered until the meatballs are fully cooked, about 45 minutes. Stir in the remaining ¾ teaspoon salt and ½ teaspoon pepper.

While the soup simmers, make the cilantro pesto: In a mini food processor or a blender, combine the cilantro, mint, lime juice, olive oil, water, and salt. Process to a paste.

Ladle the soup into warmed soup bowls and top each serving with a dollop of cilantro pesto. Serve at once.