In a large pot over medium heat, melt butter and add olive oil. Add the diced onion, carrots, celery, and garlic and sauté, stirring occasionally, 7–9 minutes or until veggies are crisp tender. Veggies shouldn't be browning; reduce the heat if they are.
Meanwhile, pull the chicken from the bones and shred or chop into bite-sized pieces.
Add Italian seasoning, chicken bouillon powder, dried thyme, dried basil, dried oregano, dried parsley, salt, and pepper to the vegetables. Stir seasonings for 30 seconds.
Pour in chicken broth and add bay leaf. Bring soup to a boil. Stir in rice and return to a boil (see note 1). Cover pan, reduce the heat to low so the soup is simmering, and cook for 10–15 minutes or until rice is tender.
Once rice is tender, stir in chicken and peas to warm through, 2–3 more minutes. Season to taste with salt and pepper. Top individual bowls with minced fresh parsley, fresh thyme, and Parmesan cheese, if desired. I recommend adding about 3 tablespoons of parsley.
Notes
Note 1: To cook the rice separately, reduce the broth to 1 carton of chicken broth and follow the directions below for cooking basmati rice:
Measure the rice and rinse it in a fine-mesh sieve until the water runs clear.
Place that rice in a bowl and cover it with water to soak for about 5–10 minutes.
While the rice is soaking, fill a large pot with water and bring to a boil.
Once the water is at a rolling boil, drain the rice and add it to the pot.
Cook without reducing the heat, for 5 minutes (taste and test to make sure it is tender) and then drain and fluff with a fork.
Simply add a few spoonfuls of cooked rice into individual soup bowls.
Storage: This soup is best eaten the same day it’s made. When stored, the rice continues to absorb liquid, so it bloats and becomes too soft. If you aren’t planning on enjoying this soup the same day it’s made, I recommend either cooking the rice separately or halving the recipe.