Chicken and Cheese Soup with Green Chilies

This has been one of my favorite soups for years. It's kind of like a tortilla soup, but heartier and with cheese. The recipe comes from the Dairy Hollow House Soup & Bread Cookbook by Crescent Dragonwagon (best name ever). I've modified it somewhat by adding black beans and a few other things.

6 cups chicken stock
1 lb. boneless chicken breasts or 1 to 2 cups cooked, diced chicken
3 tomatoes, chopped
2-3 fresh green chilies, chopped
(or substitute one can of Ro-tel and one can of diced green chilies for the tomatoes and green chilies)
2 tablespoons butter
2 tablespoons vegetable oil
1 large onion, diced
3 cloves garlic
1/2 to 1 whole fresh jalapeno, diced
2 teaspoons ground cumin
2 teaspoons chili powder
1 teaspoon chipotle sauce or powder (optional)
1 can black beans
1/2 cup flour
1 cup milk or half-and half
12 ounces grated sharp cheddar
salt and pepper, to taste
chopped cilantro for garnish

Boil chicken breasts in chicken broth until cooked through. Remove chicken and strain broth back into the pan. Let chicken cool, then dice.
Add tomatoes or Ro-tel  to chicken broth and bring it back to a boil.
Meanwhile, saute onion in butter and oil in a large skillet until translucent. Add garlic and chilies and let cook for another 2-3 minutes, then add spices. Blend in flour, a bit at a time. Gradually add milk or half-and-half and stir until smooth and thickened.
Put a ladle of chicken broth into skillet and stir. Then add skillet's contents, along with the black beans, to soup pot and cook at a bare simmer over low heat, stirring often, for 15 minutes.
Slowly stir in the grated cheese and cook until it's blended and fully melted, about 5 minutes. Add chicken and cilantro, and season with salt and pepper. Add hot sauce if it's not spicy enough.

Serve with more cilantro, lime wedges, avocados and lots of tortilla chips.