Season the chicken breasts with salt and black pepper on both sides.
In a large skillet, heat olive oil over medium heat. Add the chicken breasts and cook for about 5-6 minutes on each side, until golden brown. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and sauté for about 3-4 minutes until translucent. Add the minced garlic and cook for an additional minute.
Stir in the rice, chicken broth, heavy cream, paprika, thyme, and cayenne pepper (if using). Bring the mixture to a boil.
Once boiling, reduce the heat to low and return the chicken to the skillet. Cover and simmer for 20-25 minutes, or until the rice is cooked and has absorbed most of the liquid.
In the last 5 minutes of cooking, stir in the frozen peas and carrots. Cover and allow to finish cooking.
Remove from heat and let it sit for 5 minutes before serving. Garnish with chopped parsley.