Chicken and Rice Soup

1 teaspoon kosher salt plus more to taste

Freshly ground black pepper to taste

2 tablespoons unsalted butter

2 stalks celery , trimmed, diced

2 medium leek s, light green and white part only, diced

2 medium carrot s, diced

10 sprigs flat-leaf parsley plus

3 tablespoons finely chopped flat- leaf parsley leaves

3 sprigs fresh thyme

1 bay leaf

6 cups chicken broth, homemade or low-sodium canned

1/3 cup converted long grain rice , cooked according to package instructions