Pat chicken thighs dry and season with salt, pepper, and paprika on both sides.
Heat olive oil in a large pot or Dutch oven over medium-high heat and sear chicken skin-side down until crisp and golden, 5–7 minutes; flip and cook 4–5 minutes more.
Remove chicken and set aside. Reduce heat to medium and cook chopped onion in the same pot for 2–3 minutes, scraping browned bits.
Add minced garlic and sauté until fragrant, about 30–60 seconds.
Stir in rinsed rice, coating grains, and toast for about 1 minute until edges look translucent.
Pour in chicken broth, add dried thyme, salt, and pepper, then spread rice evenly.
Place seared chicken thighs on top of rice, skin-side up, along with any juices.
Bring to a gentle boil, then cover and reduce heat to low. Simmer 25–30 minutes until rice is tender and chicken reaches 165°F.
During last 5 minutes, lift lid and scatter frozen peas over rice. Cover again until peas are heated through.
Remove from heat and let stand covered for 5 minutes to finish steaming.
Fluff rice gently with a fork, garnish with chopped parsley, and serve warm.