Heat olive oil in a large deep skillet or Dutch oven over medium-high heat until shimmering.
Season the chicken thighs with kosher salt and black pepper on both sides.
Place the chicken thighs skin-side down in the hot oil and cook without moving for 6-7 minutes until the skin is golden brown and crispy.
Flip the chicken thighs and cook for another 4-5 minutes. Remove chicken from the skillet and set aside.
Reduce heat to medium. Add the chopped onion to the skillet and sauté for 3-4 minutes until softened and translucent.
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, onions, and garlic.
Pour in the chicken broth, heavy cream, dried thyme, and dried oregano. Stir to combine.
Return the chicken thighs to the skillet, placing them on top of the rice mixture, skin-side up.
Bring the liquid to a gentle simmer, then cover the skillet with a tight-fitting lid.
Reduce heat to low and cook for 20 minutes without lifting the lid.
After 20 minutes, remove the lid and check the rice for doneness. If rice is tender and liquid is mostly absorbed, proceed; if not, cover and cook for an additional 3-5 minutes.
Stir in the grated Parmesan cheese and thawed peas gently into the rice mixture.
Cover and cook for another 2 minutes to warm the peas and melt the cheese.
Remove from heat and let the dish rest covered for 5 minutes before serving.