Preheat the broiler and set a rack in the top third of the oven. On a baking sheet, add the tomatillos, poblanos, and jalapeno; broil, turning the chiles occasionally with tongs, until the skins of the chiles are blackened and the peppers have softened, 14-16 minutes. Remove and let cool slightly, then seed and stem the peppers and remove and discard their skins.

Transfer the tomatillos and the flesh of the chiles to a blender; blend until almost smooth. Set aside.

In a 4-quart Dutch oven or heavy-bottomed pot, heat the oil over medium-high heat. Add the onion, garlic, cumin, black pepper, and salt and cook, stirring occasionally, until the onions are softened, 6-7 minutes. Add the tomatillo mixture and chicken stock and bring to a simmer over medium-high heat. Add the hominy, shredded chicken, and spinach; cook, stirring occasionally, until the spinach is wilted and the flavors have melded, 10-15 minutes. Taste and adjust the seasoning as needed. Add a little more chicken stock if needed to loosen the consistency.

Meanwhile, crisp the chorizo: In a small skillet over medium heat, add the cubed chorizo and cook, stirring occasionally, until well browned and crispy in places, about 14 minutes.

Ladle the posole into bowls and top with the chorizo, cheese, radishes, and cilantro leaves to taste. Serve immediately with tortilla chips.