Pat oxtails dry and season generously with salt, pepper, smoked paprika, garlic powder, and onion powder.
Heat avocado oil in a heavy pot over medium-high heat. Sear oxtails on all sides until deeply browned. Remove and set aside.
In the same pot, add butter. Sauté onion and bell pepper until softened, about 3-4 minutes. Add garlic and cook for 30 seconds. Stir in tomato paste and cook for 1-2 minutes until slightly darkened. Pour in beef stock, scraping up any browned bits. Add thyme, bay leaf, and cayenne.
Return oxtails to the pot. Bring to a simmer, cover, and cook on low for 2.5-3 hours, until tender. Remove oxtails and set aside.
To prepare the rice, bring the braising liquid back to a gentle boil. Stir in rinsed Carolina Gold rice, butter, and salt. Mix well, then nestle oxtails back into the pot. Cover and cook on low for 15-18 minutes, until rice is tender and liquid is absorbed.
Remove from heat and let rest, covered, for 5 minutes. Fluff rice gently and spoon over the oxtails. Serve hot.