Mom's Broccoli Cheese Soup

Bring chicken broth to a simmer in a large pot. Add both heads of broccoli and carrots to the simmering stock; simmer for 5 minutes.

Meanwhile, melt butter in a large skillet over medium heat. Add onion and saute until softened, about 5 minutes. Stir in flour, 1 tablespoon at a time. Cook and stir until a golden roux forms, about 2 minutes. Slowly add milk, 1/2 cup at a time, stirring continuously. Bring to a boil and cook until a thickened gravy forms, about 2 minutes.

Slowly pour onion gravy into the broccoli mixture, stirring continuously. Bring to a simmer. Stir in processed cheese food. Simmer, stirring often, until cheese melts, about 5 minutes. Do not let the soup come to a boil or the cheese could separate.