In a large soup pot or Dutch oven over medium heat, brown the meat with the onions until fully cooked.
Add all of the spices and seasonings, chopped bell pepper, and garlic, and stir well to combine.
Sprinkle the flour over the ground beef mixture and stir to combine, then continue to cook over medium heat, stirring constantly, for 2-3 minutes.
Stir in the kidney beans, black beans, green chilies, salsa, enchilada sauce, chicken broth, and 1 cup of water (additional water may be added later to thin soup to desired consistency). Bring to a boil, then reduce heat and simmer for 10 to 15 minutes, stirring occasionally, until slightly thickened.
Over low heat, stir in the cubed, softened cream cheese until completely melted.
Remove the soup from the heat, then stir in the cheddar and Pepper Jack cheeses until melted. Add additional water to thin the soup, if desired.
Serve with any or all additional garnishes, although I almost never skip the diced tomatoes, onions, and cilantro, which add a great texture and flavor to the soup.