Preheat the oven to 375 degrees F. Butter a 3-quart baking dish. Melt 8 tablespoons butter in a large skillet over medium heat; add the chorizo, scallions, chiles and cumin and cook, stirring, until the chorizo is slightly browned, about 4 minutes. Add the broth and bring to a simmer.
Whisk the eggs and cilantro in a large bowl. Add the tortilla chips, bread and cheese and season with salt and pepper. Slowly pour in the chorizo-broth mixture and toss to combine. Transfer the stuffing to the prepared baking dish; dot with the remaining 1 tablespoon butter. Cover with aluminum foil and bake 30 minutes, then uncover and bake until golden, about 30 more minutes.
If you're using fresh bread, dry the cubes in a 300 degrees F oven for 15 to 20 minutes.