Heat oven to 350°F. Grease a 9x13-inch baking dish.
Warm olive oil in a large skillet over medium heat. Soften onion for 3–4 minutes.
Add chicken to the skillet. Season with salt and pepper. Brown lightly, 4–5 minutes. Remove from heat.
Whisk broth, both soups, cream cheese, melted butter, Italian mix, garlic, and sour cream in a large bowl until smooth.
Spread uncooked rice evenly in the prepared dish. Scatter chicken and onions over the rice.
Pour the creamy sauce over everything. Tap the pan to settle the liquid.
Cover tightly with foil and bake for 45 minutes.
Uncover, stir gently, and sprinkle Parmesan on top. Bake 12–15 minutes more, until rice is tender and chicken is 165°F.
Rest 10 minutes. Fluff the rice and garnish with parsley before serving.