In a dutch oven, stock pot or a large skillet, add the oil, butter, carrots, celery, onion, and garlic. Cook for 3 minutes over medium heat. Add the flour. Stir and cook for 2 minutes.
Stir in the chicken broth. Mix until combined.
Mix in the potatoes and seasonings. Turn the burner to high heat and bring to a boil. Turn heat down to medium, cover the pot and simmer soup for 15 minutes, or until the potatoes are fork-tender.
Take soup off of heat. Add the shredded chicken, cheddar cheese, and heavy cream. Stir well.
Sprinkle soup with chopped fresh parsley, or serve without garnish.
Notes
Make ahead up to 2 days in advance and store in the refrigerator until ready to serve.
Store leftovers in an airtight container in the refrigerator for up to 3 days. Reheat in a microwave-safe bowl.
Use a freezer-safe container to store leftover soup in the freezer for up to 3 months. Keep in mind that the cream may change its consistency once frozen.
Stir soup frequently to prevent potatoes from sticking to the bottom of the pot.
Taste before adding more salt to the recipe.
Smaller bites of vegetables will cook faster. You may have to adjust the cooking time if veggies are larger. Using pre-cooked chicken also shortens prep and cooking time.