Season the chicken: Pat the chicken dry.
Sprinkle with salt, pepper, and paprika. This builds flavor and helps a light sear.
Sear the chicken: Heat the olive oil in a large, heavy pot or Dutch oven over medium-high heat. Add the chicken in a single layer and cook 3–4 minutes per side until lightly browned.
Remove to a plate. It doesn’t need to be cooked through yet.
Sauté the aromatics: Reduce heat to medium. Add onion, carrot, and celery with a pinch of salt.
Cook 4–5 minutes until softened. Stir in garlic and cook 30 seconds, just until fragrant.
Add spices and rice: Sprinkle in thyme and parsley. Stir in the rice and cook 1 minute to lightly toast the grains.
Deglaze and add liquid: Pour in the chicken broth, scraping the bottom of the pot to release any browned bits.
Add the bay leaf. Taste the broth and adjust salt if needed; it should taste well-seasoned.
Nestle the chicken: Return the chicken (and any juices) to the pot on top of the rice mixture.
Simmer and cook: Bring to a gentle simmer. Cover with a tight-fitting lid, reduce heat to low, and cook for 18–22 minutes, until the rice is tender and most liquid is absorbed.
Add peas and rest: Remove from heat.
Sprinkle in the frozen peas and gently fold them in. Cover and let the pot rest for 5–7 minutes to finish steaming.
Finish and serve: Remove the bay leaf. Squeeze in a little lemon juice and sprinkle Parmesan, if using.
Fluff the rice, taste, and adjust seasoning. Serve warm.