Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
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 for 5-7 minutes until the skin is golden brown and crispy. Flip and cook for another 3-4 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.
Add the minced garlic and cook for 30 seconds until fragrant.
Stir in the rinsed rice, coating it well with the onion and garlic mixture.
Pour in the chicken broth, heavy cream, dried thyme, paprika, and crushed red pepper flakes. Stir to combine.
Return the chicken thighs to the skillet, placing them on top of the rice mixture, skin-side up.
Bring the mixture to a gentle boil, then reduce heat to low. Cover the skillet with a tight-fitting lid and simmer for 25 minutes, or until the rice is tender and the chicken is cooked through (internal temperature of 165°F).
Remove the skillet from heat. Sprinkle the grated Parmesan cheese over the rice and chicken. Cover and let sit for 5 minutes to allow the cheese to melt and flavors to meld.
Garnish with chopped fresh parsley before serving.