Heat 1 1/2 Tbsp olive oil in a 12-inch skillet over medium-high heat. Add onion, carrots and celery and saute until tender, about 8 - 9 minutes. Transfer to a plate.
Heat remaining 1/2 Tbsp oil in same skillet over medium-high heat. Add in chicken and cook 3 minutes. Add garlic and cook until chicken is nearly cooked through, about 2 minutes longer.
Add in rice, chicken broth and thyme and season with salt and pepper to taste. Return veggies to skillet.
Bring mixture to a boil then reduce heat to medium-low. Cover with lid and simmer until liquid has been absorbed and rice is nearly tender, about 18 - 20 minutes.
Stir in peas and cream, cover and cook until rice is fully tender, about 5 minutes longer.
Stir in parmesan and parsley. Serve warm.
Want it cheesier? Feel free to add more parmesan if you like it extra cheesy.
You're welcome to add different veggies to this creamy chicken and rice. Just keep in mind that onion, celery, and carrots all take a while to cook so if you add softer, faster cooking veggies (like broccoli) you may want to add them near the end of the cook time.