Heat oil in a large skillet over medium-high heat. Cook oxtail for 4 minutes. Flip and continue cooking until browned on all sides, about 4 minutes. Transfer oxtail to a slow cooker.
Add potatoes, carrots, celery, onion, tomato sauce, beef broth, red wine, parsley, Worcestershire sauce, thyme, and paprika.
Cook on Low for 7 hours. Add mushrooms and peas. Cook for 1 additional hour.