Begin by rinsing the Oxtail pieces and cutting the Vegetables. Keep a pot (high soup pot preferably) ready with the olive oil and fry the onions first gently till they are glossy. Add the garlic, carrot and potato and stir fry them along for 1-2 mins till brown.
Continue adding in first the Oxtail pieces and right after the Tomatoes and the Tomato paste and stir often or everything will burn on. Cook 2 mins and pour into the pot the red wine. Add the Beef stew or water, cook till it boils on high heat and keep it then to simmer on a lower flame level and don't forget to skim it already at this stage.
Flavour the soup with all the above mentioned herbs and pepper corns. Let it simmer on slow heat for minimum 3 hours, so that the flavours come out and mix into the soup and because the meat on the oxtail pieces requires time to soften. Check in between always if there is still enough liquid in the pot and add in around 1-2 cups of water to keep it liquid, if needed.
After 3 hours skim the soup and taste it. The Madeira is added at this stage to the dish to complete it. Remove the Oxtails and any bone pieces from the soup. The meat from the Oxtail should be soft too and easy to remove. Cut it into small pieces or cubes and add the meat to the soup. Serve hot with a glass of red wine.