Cheesy Broccoli and Vegetable Soup

1 (16 ounce) package frozen California mixed vegetables (cauliflower, broccoli, and carrots)

1 (16 ounce) bag frozen broccoli

2 (14.5 ounce) cans chicken broth

¼ cup butter

½ cup all-purpose flour

2 cups milk

1 (1 pound) loaf processed cheese food (such as Velveeta®), cubed

Place the mixed vegetables and frozen broccoli into a large pot. Pour in the chicken stock and bring to a boil. Reduce heat to medium-low and simmer until the vegetables are tender, about 20 minutes. Meanwhile, melt the butter in a saucepan over medium heat; stir in the flour until smooth and cook for a few minutes until the color lightens slightly. Whisk in the milk and simmer until thickened, about 10 minutes. Stir in the cheese until melted; stir the cheese mixture into the simmering vegetables. Cook and stir until the vegetables are tender, about 5 minutes more.