In a large soup pot, add the chicken and broth, bring to a boil, and simmer until the chicken is cooked through.

Because the pieces of chicken are small, this won’t take more than about 5 minutes.

Using a slotted spoon, remove the cooked chicken and set aside for now.

Add the carrots, celery, onion, mushrooms, parsley, and rosemary to the pot and bring to a boil once again.

Lower the heat, cover the pot, and simmer until the vegetables are tender, about 10-15 minutes.

Again using the slotted spoon, transfer about half of the cooked vegetables to a food processor or blender and puree.

Return the pureed vegetables to the soup pot along with the cooked chicken, and keep the heat on fairly low—you don’t want the soup to boil but you do want it to be hot.

In a small saucepan, melt the butter and add the flour, stirring constantly.

Cook and stir for about 30 seconds and then—still stirring constantly—gradually add the milk.

Cook until the mixture thickens and then add it to the soup, along with the peas.

Simmer for several minutes more until the peas are hot.

If you use frozen peas, you’ll have to simmer the soup for a bit longer.

Before serving, add salt and pepper to taste.