To prepare a homemade version of the broccoli cheese soup from Jason's Deli, combine 1 package of store-bought broccoli Cheddar soup, such as the Bear Creek brand, 2 cups of chicken broth, 2 cups of water, 2 cups of skim milk and 1 cup of broccoli chopped into small pieces. Bring the broth, water and milk to a gentle boil, stir in the soup mix, simmer the soup for about eight minutes, and add the chopped broccoli.
Blend the soup to achieve a smoother consistency. Alternatively, to make the soup from scratch, sauté 1 diced onion and 2 diced celery stalks in 1/2 stick of butter in a large stock pot until the onions are translucent. Add 3 cups of chicken stock, 1 cup of half and half, 2 large chopped stalks of broccoli and 2 finely chopped carrots. Bring the mixture to a boil, reduce the heat, and simmer for 10 to 15 minutes.
In a separate bowl, whisk together 1/3 cup of cornstarch and 1 1/2 cup of milk, and add the well-mixed concoction to the soup. Stir the soup for about three to four minutes or until it begins to thicken. Add 1/2 teaspoon of salt and 1/4 teaspoon each of black pepper, garlic powder and thyme. Lower the heat, and stir in 8 ounces of Velveeta cheese, cubed, and 1 1/2 cups of shredded Cheddar cheese. Continue stirring until all of the cheese melts.