Cook broccoli according to package directions.

Drain any liquid from the cooked broccoli.

Chop the broccoli into very fine pieces, using a knife or food processor.

Warm 1/2 cup of chicken broth in a Dutch oven over medium heat.

Once the broth is simmering, whisk in the flour to create a smooth paste.

Add the remaining chicken broth, cooked broccoli, heavy whipping cream, American cheese, dried onion, and black pepper to the pot.

Heat the soup until all the cheese is melted and the mixture is well combined.

Add the shredded cheddar cheese and stir until melted.

Simmer the soup for about 5 minutes, or until it thickens to your desired consistency.

Serve hot.