Up to two days ahead, tip the oxtail into a bowl and season with a little salt. Tie the thyme sprigs, bay leaves and parsley stalks together and put in the bowl with the peppercorns and star anise. Pour over the wine, then cover and chill for up to 48 hrs.
Heat oven to 160C/140C fan/gas 4. Lift the oxtail out of the marinade, reserving the mixture. Heat a drizzle of the oil in a large casserole pan and, in batches if needed, brown the oxtail. Transfer to a plate and set aside. Add another drizzle of oil and cook the carrots, onion, celery and garlic until just starting to brown. Stir in the flour and ketchup and cook until you have a thick paste. Pour over the reserved marinade and simmer for 1 min. Nestle the oxtail back in the pan and pour over as much stock as you can, chilling any extra to use later. Bring everything to a gentle boil, scoop off any froth then cover and place in the oven for 3 hrs 30 mins, stirring once or twice until the meat is very tender.
Remove the soup from the oven and leave to cool slightly, then lift the oxtail from the broth and shred the meat using two forks. Discard the bones and transfer the meat to a bowl. Sieve the liquid into another bowl, then cover and chill overnight.
Remove and discard any fat that has solidified on top of the soup. Tip the broth into a saucepan and simmer until silky, adding more stock if the broth is too thick. Stir through the shredded meat until warmed through. Season to taste, then ladle into bowls and scatter over some parsley leaves, if you like.