To a large pot, add the oil and butter over medium heat. Allow that to get hot after 2 to 3 minutes.
You will then add your onion, carrots, and celery. Cook for 7 minutes while stirring occasionally.
Add the minced garlic and stir for 1 minute.
Add the flour and stir for 2 minutes.
Next, add the chicken broth, chicken, and seasonings. Bring to a boil, then reduce the heat to a low simmer and cook for 7 minutes, or until the chicken starts to fall apart.
Remove the bay leaves and discard.
Use 2 forks to shred the chicken directly in the pot, or remove it and transfer it to a cutting board to shred. Transfer that back into the pot.
Heat the milk and heavy cream in the microwave for 20 seconds to take the chill off.
Add 1 cup of rice at a time, along with ¼ cup of milk and ¼ cup of heavy cream. Stir until combined.
Add the remaining rice and stir. Simmer on low for 10 minutes, as it will start to thicken.
You can add more milk or heavy cream to make the soup creamier or to thin it out.
Taste to see if salt and pepper are needed.
Top with parsley.
Notes
You can keep this in the fridge for up to 3-4 days. It will thicken after being refrigerated. You can add more broth to thin it out.
This recipe was calculated using the exact brands and measurements I used to make this recipe. If you are following a strict diet please note changing anything will cause the nutritional info to change. My calculations are intended as a guide only.