Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Season the chicken thighs with salt and black pepper on both sides.
Place the chicken thighs skin-side down in the hot oil and cook for 5-7 minutes until the skin is golden brown and crispy. Flip and cook for another 3 minutes. Remove chicken from the pan and set aside.
Reduce heat to medium and add the chopped onion to the pan. Cook for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Stir in the rinsed rice, smoked paprika, ground cumin, and dried thyme. Cook for 1-2 minutes, stirring frequently, to toast the rice and spices.
Pour in the chicken broth and stir to combine, scraping up any browned bits from the bottom of the pan.
Return the chicken thighs to the pan, placing them skin-side up on top of the rice.
Bring the mixture to a gentle simmer, then reduce heat to low. Cover the pan with a lid and cook for 25 minutes without lifting the lid.
After 25 minutes, remove the lid and sprinkle the frozen peas over the rice. Cover and cook for an additional 5 minutes until the peas are heated through and the rice is tender.
Remove the pan from heat and let it rest, covered, for 5 minutes.
Garnish with chopped fresh parsley before serving.