In a shallow dish, whisk flour, 1 teaspoon of chile powder and salt. Coat beef with flour mixture; reserve unused flour.
Heat oil in a large pot or Dutch oven over medium-high heat. Add beef and cook, turning, until all sides are browned, about 5 minutes. Remove to a plate and reserve.
Add onion and garlic to pot and cook over medium heat, stirring to keep garlic from burning, about 4 to 5 minutes. Sprinkle with 1/4 cup water, if needed. Scrape up any browned bits from bottom of pot.
Stir in beef and any accumulated juices, reserved flour mixture, broth, tomatoes, 1 cup water and dried oregano. Bring to a boil. Reduce heat to medium-low. Gently simmer 1 hour, stirring occasionally.
Add hominy, carrots, green pepper and remaining 1/2 teaspoon chile powder, if using. Simmer, covered, for 20 to 25 minutes or until carrots are tender.
Stir in cilantro and serve with cooked brown rice.