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.
Recipe source: Cooking Classy