Place chiles in a small saucepan with 2½ cups water. Bring to a boil, remove from heat and steep chiles for 30 minutes. Place softened chiles and about ½ cup of the liquid in a food processor or blender. Process until smooth, adding additional liquid if necessary to puree. Pass mixture through a strainer to remove seeds and any bits of skin.
Heat oil in a large saucepan over medium-high heat. Add meat and brown evenly. Add onions, peppers and garlic, and cook until onions are translucent.
Add tomatoes, canned chiles, oregano, beef broth and processed chiles. Cover and bring to a boil. Reduce heat to low, and simmer for 2 hours or until meat is tender. While cooking, make sure that there is always enough liquid to barely cover meat. Season to taste with salt and pepper.
To serve, ladle chile into bowls, and serve with warm flour tortillas, cheese, salsa and chopped onions on the side. Guests can spoon chile onto tortillas and add desired toppings.
