Rinse the rice under cold water until the water runs clear. Cook the rice in chicken broth according to package instructions until tender and fluffy. Set aside.
Heat olive oil in a large skillet over medium heat.
Add the diced onion and sauté for about 2–3 minutes until soft and translucent.
Stir in the minced garlic and cook for 1 minute until fragrant.
Season the chicken breasts evenly with paprika, salt, black pepper, and dried thyme.
Place the chicken in the skillet and sear for 5–6 minutes per side until golden brown and fully cooked.
Remove the chicken from the skillet and set aside.
Pour the heavy cream into the skillet, stirring while scraping the browned bits from the bottom of the pan to build the sauce.
Let the cream gently simmer for a few minutes until slightly thickened.
Add the frozen peas if using and cook for 2–3 minutes.
Return the chicken to the skillet and let it simmer in the sauce for about 5 minutes so all the flavors combine into the creamy smothered chicken and rice.
Serve the creamy chicken over the warm rice and garnish with parsley.