Combine 6 Roma tomatoes, 1/2 onion, chipotle peppers, and garlic in a blender. Process until smooth.
Heat oil in a soup pot over medium heat. Add tomato mixture to hot oil. Cook until color changes, about 5 minutes. Add chicken stock; reduce heat and simmer soup until ready to add meatballs, about 10 minutes.
Combine beef and pork in a bowl. Add 3 chopped Roma tomatoes, chopped onion, egg, rice, mint, oregano, salt, and pepper. Mix well, using your hands, until uniform. Use clean, wet hands to form mixture into balls 1/4 cup at a time. Place on a baking sheet.
Bring soup to a rolling boil. Place a meatball into a ladle; submerge and release it into the boiling liquid. Repeat with remaining meatballs.
Stir potatoes and zucchini into the soup and return to a boil. Reduce heat, season with salt, and cover the pot. Simmer until meatballs are no longer pink and vegetables are tender, about 30 minutes.