Pat the chicken thighs dry with paper towels. Season both sides with the fine sea salt, black pepper, paprika, and garlic powder, rubbing the spices into the skin and meat so they adhere well.
Heat the olive oil in a large deep skillet or wide saucepan over medium-high heat. When the oil is hot and shimmering, add the seasoned chicken thighs skin-side down and sear for 4–5 minutes, until the skin is golden brown and crisp. Flip and sear the other side for another 3–4 minutes. Transfer the chicken to a plate and set aside, leaving the drippings in the pan.
Reduce the heat to medium and add the unsalted butter to the same pan. Once the butter has melted, add the finely chopped yellow onion. Cook, stirring often, for 3–4 minutes until the onion softens and turns translucent.
Stir in the minced garlic and cook for about 30 seconds, just until fragrant, being careful not to let it brown.
Add the rinsed long-grain white rice to the pan. Stir well to coat the rice in the butter, onion, and garlic mixture, toasting it lightly for 1–2 minutes so the grains become glossy and slightly nutty in aroma.
Pour in the low-sodium chicken broth and stir, scraping up any browned bits on the bottom of the pan. Add the dried thyme, dried oregano, and crushed red pepper flakes if using. Stir again to distribute the seasonings evenly in the liquid.
Return the seared chicken thighs to the pan, placing them skin-side up on top of the rice mixture. Nestle them in gently so they sit partly in the liquid but the skin is not submerged.
Bring the mixture to a gentle simmer, then reduce the heat to low. Cover the pan with a tight-fitting lid and cook for 18–20 minutes, without lifting the lid, until most of the liquid is absorbed and the rice is nearly tender.
Remove the lid and pour the heavy cream evenly around the chicken and over the rice. Sprinkle the grated Parmesan cheese over the top. Gently shake the pan or use a spoon to nudge the cream and cheese into the rice without fully submerging the chicken skin.
Cover the pan again and continue to cook on low heat for another 5–7 minutes, until the rice is creamy and tender, the sauce has thickened slightly, and the chicken thighs are cooked through.
Turn off the heat and let the dish rest, covered, for 5 minutes to allow the rice to finish steaming and the sauce to settle. Uncover and sprinkle the chopped fresh parsley evenly over the chicken and rice.
Serve the Creamy Smothered Chicken and Rice straight from the pan, making sure each portion includes a chicken thigh, a generous scoop of creamy rice, and some of the sauce from the bottom of the skillet.