Easy Broccoli Cheese Soup

Name: Easy Broccoli Cheese Soup
Prep time: 30 min
Cook time: 15 min
Total time: 45 min
Cuisine: American
Ingredients: 3 1/2 cups chicken broth (I use low-sodium); 1/2 cup finely diced onion (white or yellow); 1 teaspoon salt; 1/2 teaspoon pepper; 5-6 cups about 30-36 ounces chopped fresh broccoli (see note); 4 cups milk (I use 2%); 1/2 cup all-purpose flour (use 2/3 cup if you want it extra thick); 3 cups freshly grated cheddar cheese (see note); 1 cup freshly grated Swiss cheese (see note)