Preheat an oven to 425 F. Line a small baking sheet with parchment paper.
Toss the quartered tomatoes and garlic cloves with 2 tablespoons of olive oil and season with salt and pepper. Pour them onto the tray and group everything together in the center (this keeps the garlic from burning!). Roast for 25 minutes, until the tomatoes are blistered. Transfer to a blender with the chile de arbol and blend until smooth.
Heat the remaining olive oil in a large dutch oven or soup pot over medium heat. Add the white onion and tomato mixture and cook for 3-4 minutes, until some of the liquid has evaporated. Add the chicken stock, bouillon, carrots, and potatoes to the pot and bring to a simmer. Add the meatballs, cover, and simmer for 30 minutes.
Add the zucchini and green beans to the pot and simmer for another 5-10 minutes, until the veggies are just barely tender without being mushy. Season the soup to taste with salt and pepper and stir in the cilantro. Ladle into bowls and serve with limes and tortillas on the side for dipping.