In a large skillet, heat the olive oil over medium-high heat. Season the chicken breasts with salt and pepper, then add them to the skillet. Cook for about 5-7 minutes on each side until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion and sauté for about 3-4 minutes until softened. Add the minced garlic and cook for an additional 1 minute until fragrant.
Stir in the rice, chicken broth, heavy cream, thyme, and paprika. Bring the mixture to a boil, then reduce the heat to low and cover. Simmer for about 15 minutes, or until the rice is tender and has absorbed most of the liquid.
Add the frozen peas and carrots to the rice mixture, stirring to combine. Place the cooked chicken breasts on top of the rice, cover, and cook for an additional 5 minutes to heat through.
Remove from heat and let it sit for a few minutes before serving. Garnish with chopped parsley.