In a large heavy pot, heat 1 tablespoon of the vegetable oil over medium-high heat. Add the onion and sauté until translucent, about 5 minutes. Add the parsley and cook for 1 minute. Season with salt and pepper. Let cool slightly.

Mix the rice, ground meat, 2 teaspoons salt, and ½ teaspoon pepper in a large bowl. Add the sautéed onion mixture and mix until incorporated. Using wet hands, shape into 20 meatballs, each about 1 inch in diameter.

Add the remaining 1 tablespoon oil to the same pot and sauté the carrot and serrano for 5 minutes. Mix in the tomato paste and vegetable stock, and bring to a boil. Add the meatballs, potato, and zucchini. Simmer over low heat for 30 minutes until the meatballs are cooked through.

Season the soup with salt and pepper before ladling into bowls.