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.
Photograph by David Malosh