Beefy Broccoli and Cheese Soup

2 cups chicken broth (I use one can of broth with water and one bouillon cube to make 2 cups)
1 pkg. (10 oz.) frozen, chopped broccoli (I sometimes use fresh, about 2 cups)
1/4 cup chopped onion
1/4 cup browned ground beef
1 cup milk
2 Tbsp. flour
1 cup shredded sharp cheddar cheese
1/2 tsp. dried oregano leaves
salt and pepper

Bring broth to a boil; add broccoli and onion. Cook five minutes until broccoli is tender. In a bowl, gradually add milk to the flour until smooth. (I sift it in slowly so it doesn't clump.) Add milk mixture and beef to the broth mixture. Cook on medium heat, stirring constantly until thick and bubbly. Add cheese and oregano; stir until cheese is melted. Season with salt and pepper.