Heat the oil in a heavy, large pot over medium heat. Add the onions, potatoes, yams, garlic, tomatillos and poblanos. Cover and sweat until the onions are tender, stirring often to prevent browning, about 8 minutes. Mix in the oregano, flour, cumin, 1 teaspoon salt and 1/2 teaspoon pepper. Add the hominy with the juices and the broth and bring the chili to a simmer.
Place the green chiles in a processor. Using tongs, transfer strips of the poblano chile from the pot to the processor; blend just until smooth. Scrape the chile sauce into the pot.
Cover and simmer the chili 20 minutes. Uncover and simmer until the potatoes and yams are tender and the chili is reduced to desired consistency, stirring often, 20 to 25 minutes longer. Season with more salt and pepper if desired.
Ladle the chili into bowls. Serve with garnishes and Buttermilk and Sour Cream Corn Bread.
Position a rack in the center of the oven and preheat to 400 degrees F. Butter a 9-by-9-by-2-inch metal baking pan.
Blend the cornmeal, flour, sugar, baking powder, salt and baking soda in a processor for 5 seconds. Add the butter cubes. Blend until the butter is reduced to tiny pieces, 15 to 20 seconds. Whisk the buttermilk, sour cream and eggs in a large bowl to blend. Add the dry ingredients from the processor and stir until evenly moistened. Scrape the batter into the prepared pan.
Bake the corn bread until the top is golden brown and a tester inserted into the center comes out clean, about 25 minutes. Cool the bread on a rack at least 30 minutes. Serve warm or at room temperature.