Season the cubed chicken generously with salt and pepper. In a large, deep skillet or Dutch oven, heat olive oil until shimmering. Add the chicken and sear until nicely browned on all sides, about 4-5 minutes. Remove to a plate.
Reduce heat to medium. Add butter to the skillet (do not wipe it out). Add onion, carrots, and celery. Sauté for 5–7 minutes until softened. Stir in garlic and cook for 1 minute.
Add the brown rice to the skillet. Stir constantly for 2–3 minutes to toast. Sprinkle in thyme and paprika.
Pour in chicken broth, scraping up any browned bits. Add bay leaf and return chicken to the pot. Nestle chicken into the rice and liquid. Bring to a boil, then reduce heat to low, cover, and simmer gently.
Cook untouched for 35–40 minutes until liquid is absorbed and rice is tender.
Remove from heat. Stir in frozen peas and parmesan cheese. Cover and let rest for 10 minutes. Garnish with parsley before serving.