Make the tomatillo salsa: Preheat the broiler. Remove the husks from the tomatillos, then rinse the tomatillos under warm water to remove any stickiness. Dry with a paper towel. Put the tomatillos, chiles, garlic and sliced onion on a rimmed baking sheet. Drizzle with the olive oil and sprinkle on 2 teaspoons or so of salt. Broil a few inches from the heat, turning everything once, until the tomatillos are softened and slightly charred, about 7 minutes. Let cool to room temperature.
Transfer the broiled vegetables to a blender; add the cilantro and puree until smooth. Season with salt and pepper.
Make the chili: Heat the olive oil in a Dutch oven or large saucepan over medium heat. Add the chopped onion and cook, stirring occasionally, until just translucent, about 4 minutes. Add the sausage and cook, stirring and breaking it up, until browned, about 10 minutes.
Spoon out and discard the excess fat, leaving 1 to 2 tablespoons in the pot. Stir in the oregano and garlic and cook, stirring, about 3 more minutes.
Stir in the tomatillo salsa, hominy (including the liquid), cilantro and pumpkin. Bring to a boil, reduce the heat to medium low and simmer, covered, until the pumpkin is tender, 15 to 20 minutes. Taste and season with salt, if necessary. Top with cilantro and chiles.