Heat olive oil and butter in a large, oven-safe skillet over medium-high heat. Add chicken and cook until browned on all sides, about 5-7 minutes. Remove chicken and set aside.
Add mushrooms and onion to the same skillet. Cook until mushrooms release their liquid and start to brown, about 5 minutes. Add garlic and thyme and cook for 1 minute more until fragrant.
Sprinkle flour over the mushroom mixture and stir constantly for 1 minute to cook out the raw flour taste.
Slowly whisk in the chicken broth until smooth. Bring the mixture to a simmer.
Stir in the uncooked rice. Return the chicken to the skillet, nestling it into the liquid.
Reduce heat to low, cover the skillet, and simmer for 15-20 minutes, or until the rice is tender and most of the liquid is absorbed. Do not lift the lid during this time.
Remove the skillet from the heat. Stir in the heavy cream and cream cheese until the sauce is smooth and creamy.
If using, stir in the frozen peas. Cover and let stand for 5 minutes to allow the peas to heat through.
Garnish with fresh parsley before serving directly from the skillet.
Notes
For a richer flavor, use chicken broth instead of water to cook the rice.
If the sauce seems too thick after adding the cream cheese, add a splash more broth or milk until you reach your desired consistency.
You can substitute heavy cream with half-and-half for a slightly lighter sauce.