Heat the vegetable oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Stir in the chili powder. Add the squash, poblano, oregano, cumin, garlic and 1/2 teaspoon salt and cook, stirring frequently, until the poblano softens slightly, about5 minutes. Add 5 cups water, the tomato puree and 1/2 teaspoon salt; cover and bring to a simmer. Uncover and cook until the squash is tender, about 15 minutes, adding the hominy during the last 2 minutes of cooking.
Season the posole with salt and divide among bowls. Top with the avocado and salsa and sprinkle with oregano. Serve with chips.
Photograph by Justin Walker
Recipe courtesy Food Network Magazine