Searing the Oxtail: Generously season the oxtail pieces with salt and pepper. Heat olive oil in a wide, heavy-bottomed skillet over medium-high heat. Working in batches if necessary, sear the oxtail on all sides until a deep, caramelized crust forms. This browning step adds a robust depth of flavor that carries through to the finished dish. Set the seared oxtail aside.
Preparing the Vegetables: While the meat is searing, chop the onion, carrots, and celery into uniform pieces for even cooking. Mince the garlic finely to help it melt seamlessly into the sauce. Once the oxtail is browned and removed from the skillet, proceed to the aromatics.
Sautéing the Aromatics: In the same skillet used for browning the oxtail, add the chopped onion, carrots, and celery. Cook over medium heat for around 5 minutes, stirring occasionally, until the vegetables begin to soften and release their aroma. Stir in the minced garlic and tomato paste, continuing to cook for 1 to 2 more minutes, allowing the tomato paste to darken and the garlic to become fragrant.