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 golden and crisp, about 5–7 minutes; flip and cook 4–5 more minutes. Remove and set aside.
Lower heat to medium and sauté chopped onion in the same pot for 2–3 minutes, scraping up browned bits.
Add minced garlic and cook until fragrant, about 30–60 seconds.
Stir in rinsed rice, coating it with oil and aromatics, and toast for 1 minute until edges look translucent.
Pour in chicken broth, add dried thyme, salt, and pepper; stir to combine and spread rice evenly.
Place seared chicken thighs skin-side up on top of the rice along with any juices.
Bring to a gentle boil, then reduce heat to low, cover, and simmer for 25–30 minutes until rice is tender and chicken reaches 165°F.
In the last 5 minutes, lift lid and scatter frozen peas over rice; cover and continue cooking 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.