Pat the chicken thighs dry and season both sides with salt and black pepper. Add the flour to a shallow plate.
Lightly dredge each chicken thigh in the flour, coating both sides and shaking off the excess. Discard any flour that touched the raw chicken.
Heat the vegetable oil in a Dutch oven or deep skillet over medium-high heat. Sear the chicken thighs until golden brown on the outside while still raw in the center. Transfer them to a plate.
Add the diced onion and minced garlic to the same pot. Cook until they begin to soften and brown while scraping up the browned bits from the bottom.
Add the chopped parsley and cook for about 10 seconds, just until fragrant.
Stir in the long-grain white rice and toast it briefly in the onion mixture.
Add the chicken broth, cream of chicken soup, and paprika. Stir until the soup is fully incorporated and the rice is evenly distributed.
Return the seared chicken thighs to the pot. Bring the liquid to a gentle simmer, cover, and reduce the heat to medium-low.
Cook for 20–25 minutes, or until the rice is tender and the chicken reaches 165°F in the thickest part without touching the bone. A small amount of creamy liquid should remain around the rice.
Turn off the heat and carefully remove the chicken thighs. Stir the cold butter and heavy cream into the rice until smooth and creamy.
Taste and adjust the salt and pepper, then return the chicken to the pot or serve it over the rice.