Heat the olive oil in a large skillet over medium heat. Season the chicken breasts with salt, pepper, and paprika. Add the chicken to the skillet, cooking for about 5-7 minutes on each side or until golden brown and cooked through. Remove the chicken breast from the skillet and set aside.
In the same skillet, add the chopped onion and sauté until translucent, about 3-4 minutes. Add the minced garlic and sliced mushrooms, cooking for an additional 3 minutes until the mushrooms are tender.
Stir in the rice, then pour in the chicken broth. Add the dried thyme, bring the mixture to a boil, and then reduce to a simmer. Cover and cook for about 15 minutes, or until the rice has absorbed most of the liquid.
Once the rice is cooked, stir in the heavy cream and frozen peas. Let it simmer for another 5 minutes, stirring occasionally to prevent sticking.
Return the chicken breasts to the skillet, nestling them in the creamy rice mixture to reheat. Cook together for an additional 3-5 minutes.
Adjust seasoning with salt and pepper to taste.
Remove from heat, and garnish with chopped fresh parsley before serving.
Notes
Serve in deep bowls, garnished with extra parsley and optionally sprinkle with grated Parmesan.