Heat the olive oil in a large skillet or heavy pot over medium-high heat. Season the oxtails with salt and pepper, then brown them on all sides for about 8–12 minutes. Transfer the browned oxtails to the slow cooker.
In the same skillet, add the diced onions and cook until they are softened and golden, about 5–7 minutes.
Transfer the cooked onions to the slow cooker over the oxtails.
Add the tomato paste, beef broth, bay leaves, and oregano to the slow cooker.
Cover the slow cooker and cook the oxtails on high for 4 hours or on low for 8 hours, or until they are tender and falling off the bone. Taste and adjust the salt and pepper if needed before serving. Serve the oxtails warm with mashed potatoes, rice, or crusty bread. Enjoy!