Fry oxtails in oil in Dutch Oven over medium high heat until golden brown on both sides. Add finely chopped onion, sliced carrots, salt, black pepper, bay leaf. Add water or broth so that it covers the vegetables and meat.
Cover with a lid. Put Dutch Oven in a preheated oven set to 370 F for 2 hours. Pull out. Add potatoes and put in the oven for another hour. The meat should come off the bone easily at this time.
Remove bay leaf, shred meat off bones and put back into the soup to serve.
** If you really wanted to thicken the broth when done you could. If so I would suggest at the end to use a slotted spoon to remove items, set aside and keep warm. Put broth in Dutch Oven over medium high heat on stove. In a small dish whisk together 2 tbsp cornstarch with a bit of the liquid in the pot.
Once smooth pour this into your pot of boiling broth and stir allowing the liquid to thicken to your liking. Once achieved, add the items back in. You could at this time remove the meat off of the bone and add back in that way so it is easier to eat.