Rinse rice under cold water until the water runs clear. Cook according to package directions, replacing water with chicken broth for more flavor. Set aside.
Heat olive oil in a large skillet over medium heat. Add diced onion and sauté for 2–3 minutes until translucent.
Stir in minced garlic and cook for 1 minute until fragrant.
Season chicken breasts with paprika, salt, pepper, and thyme. Place in skillet and cook 5–6 minutes per side until golden brown and cooked through (165°F internal temperature). Remove chicken and set aside.
Lower heat and add heavy cream to the skillet. Stir well, scraping up browned bits for flavor. Bring to a gentle simmer.
Add frozen peas (if using) and cook for 2–3 minutes until tender.
Return chicken to the skillet, nestling into the sauce. Simmer for 5 minutes to blend flavors.
Serve hot over cooked rice, garnished with parsley.