Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Season the chicken legs with salt, black pepper, smoked paprika, ground cumin, and dried thyme on all sides.
Add the chicken legs to the skillet skin side down and sear for 5-7 minutes until the skin is golden brown and crispy. Flip and sear the other side for 3-4 minutes. Remove chicken legs from the skillet and set aside.
Reduce heat to medium and add the chopped onion to the skillet. Sauté for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the rinsed rice to the skillet and stir to coat the rice with the oil and onion mixture.
Pour in the chicken broth and stir to combine. Bring the mixture to a gentle boil.
Return the chicken legs to the skillet, placing them on top of the rice.
Cover the skillet with a tight-fitting lid and reduce the heat to low. Simmer for 25 minutes without lifting the lid.
After 25 minutes, remove the lid and scatter the frozen peas over the rice. Cover again and cook for an additional 5 minutes until the peas are heated through and the rice is tender.
Remove the skillet from heat and let it rest, covered, for 5 minutes.
Sprinkle chopped fresh parsley over the dish before serving.