Season the oxtail pieces with salt and pepper in a large bowl. Dredge them in flour, shaking off any excess.

In a large Dutch oven or heavy-bottomed pot, heat the vegetable oil over medium-high heat. Brown the oxtails in batches on all sides until deeply caramelized. Remove them from the pot and set them aside.

In the same pot, add the diced onion, minced garlic, celery, and carrots. Sauté the vegetables until softened and lightly browned, about 5 minutes.

Deglaze the pot by pouring in the red wine and using a wooden spoon to scrape up any browned bits from the bottom. Let the wine simmer for a few minutes to reduce slightly.

Add the beef broth, diced tomatoes (with their juice), bay leaves, dried thyme, and smoked paprika to the pot. Stir well to combine.

Return the browned oxtails to the pot, nestling them into the liquid. Bring the mixture to a simmer, then reduce the heat to low and cover the pot with a lid. Let the oxtails simmer gently for 2 to 3 hours, or until the meat is fork-tender and easily falls off the bone.

Once the oxtails are cooked, remove the lid from the pot and increase the heat to medium. In a small bowl, whisk together 1/4 cup of flour with 1/2 cup of water until smooth to create a slurry. Slowly pour the slurry into the pot while whisking constantly, until the gravy thickens to your desired consistency.

Let the gravy simmer for a few more minutes to cook out the raw flour taste.

Remove the bay leaves from the pot and discard them. Serve the smothered oxtails over a bed of rice, mashed potatoes, or your favorite side dish. Garnish with freshly chopped parsley for a burst of freshness and color.