In a medium pot, bring broth, chilis, tomatoes, onion and garlic to a boil.
Cover and reduce heat to medium; simmer for 10 minutes or until vegetables are soft.
While the vegetables are cooking, using a large pot or Dutch oven, over medium heat, melt the butter.
Add the flour and cook for 3 minutes while stirring constantly.
Stir in 3-1/2 cups of the hot milk, adding a 1/2 cup at a time.
Cook 7 minutes over medium heat until thickened.
Remove vegetables/broth mixture from the heat; stir into milk mixture, 1/4 cup at a time.
Add remaining 1-1/2 cups of hot milk, salt and pepper and Monterey Jack cheese.
Stir until cheese is melted.
Make sure to not heat the cheese soup on too high or the cheese will "break" and be grainy.
Notes
When making soups, it is best to not use pre-shredded cheese which can have additives and doesn't melt as well. For creamier soups buy cheese in blocks.