Place poblanos on a foil-lined baking sheet. Broil 7 minutes on each side or until blackened and charred. Place in a paper bag; fold to close tightly. Let stand 15 minutes. Peel the chiles; cut in half lengthwise. Discard seeds and membranes. Chop coarsely. Set aside.
While the poblanos roast, place the tomatillos in a food processor, and process until smooth. Set aside.
Heat a Dutch oven over medium heat. Add oil to the pan, swirl to coat. Add onion and jalapeno, saute 5 minutes or until tender, stirring occasionally. Add garlic and cumin; saute 1 minute, stirring constantly. Add tomatillos, broth, and next 4 ingredients; bring to a boil. Cover, reduce heat, and simmer for 10 minutes or until the vegetables are tender.
Add the roasted poblanos and hominy; cook for 2 minutes or until heated through.
Ladle into 4 shallow bowls; top evenly with sour cream and cheese. Sprinkle with cilantro and serve.