Heat the oil in a large pot. Add the onion and garlic, cover, and cook, stirring occasionally, until the onion is soft, about 5 minutes.
Add the cumin and salt and cook until fragrant, about 30 seconds. Add the hominy, jalapeno, and tomatillos and cook, stirring, for 1 minute. Add the Swiss chard, stock, and bay leaves and bring to a boil.
Cover and cook, stirring, until the chard is wilted and the leaves are tender, about 20 minutes. Remove the bay leaves.
Ladle the soup into 4 bowls and garnish each serving with radishes, jalapenos, avocado, scallions, sour cream, and 2 lime wedges. Sprinkle with chile de arbol powder and top with the chopped cilantro sprigs.