How to Make It
Preheat the oven to 500°. Arrange the tomatoes on a small rimmed baking sheet. Set the unpeeled onion in a pie plate with 6 of the garlic cloves. Roast the vegetables on the top rack of the oven until blackened on top and tender, about 10 minutes for the garlic, 20 for the tomatoes and 30 for the onion. Let cool slightly, then cut the onion in half. Press the tomatoes through a coarse strainer.
In a large saucepan, cover the chicken breasts with the stock. Add the lime zest and lime halves, allspice, oregano, the remaining 15 garlic cloves and a pinch each of salt and pepper and bring to a boil over moderately high heat. Add the roasted onion, reduce the heat to low and simmer until the chicken is cooked through, about 30 minutes.
Transfer the chicken to a platter and let cool. Gently simmer the broth for 10 minutes, then strain. Wipe out the saucepan. Remove the chicken from the bones and tear it into thick shreds.
Heat 2 tablespoons of the oil in the saucepan. Add the scallions and roasted garlic; mash the cloves to a paste with a fork. Cook over moderately high heat until the scallions are browned, 4 minutes. Add the strained tomatoes and simmer until the fat separates from the sauce, about 5 minutes. Add the strained broth and bring to a boil; reduce the heat to low and simmer for 10 minutes. Season with salt and pepper.
Meanwhile, in a large skillet, heat the remaining 1 cup of oil until shimmering. Add one-fourth of the tortilla strips and fry over moderately high heat, stirring occasionally with a slotted spoon, until golden brown, about 2 minutes. Transfer to a paper towel-lined baking sheet and season with salt. Repeat with the remaining tortilla strips, lowering the heat if the oil gets too hot.
Add the chicken to the broth and cook until heated through. Ladle the soup into bowls, top with the tortilla strips and sprinkle with oregano. Serve, passing lime wedges, minced onion and banana chiles at the table.
Winter tomatoes are often cottony and flavorless, but they will ripen a bit if left out at room temperature for a few days. If you can, plan ahead and buy the tomatoes 2 to 3 days in advance of making this recipe. You could also substitute a pound and a half of cherry tomatoes, which are tasty all year. When roasting the smaller tomatoes, check them after 10 minutes. They will blacken faster than the regular tomatoes.