Prepare the vegetables by washing and setting them aside to dry.
Peel and dice the carrots, stalk of celery, and green onion. Set the green onion aside.
Peel the onions and mince them into fine pieces.
Pour ½ cup of flour onto a plate and give the oxtails a light coating.
Heat the cooking oil in a large, heavy pot over high heat. Cook to brown the meat, remove (keeping the fat in the pan), and drain on paper towels.
Add the minced onions to the pot, turn the heat to medium, and sauté 8 to 10 minutes until golden brown.
Sprinkle in the remaining 2 tablespoons flour, mix well, and brown lightly.
Slowly add the water, and stir in tomato paste, salt, and pepper. If you have a cheesecloth, place the bay leaf, thyme, cloves, and parsley in the cent and tie tightly. If you do not have cheesecloth, throw the ingredients directly into the pot.
Return oxtail to the pot, cover, and simmer 3 hours until meat is fork-tender. Cool and skim off fat; remove cheesecloth bag or remove the bay leaf, thyme, cloves and parsley.
Remove the oxtail from the soup and separate the meat from the bones. Cut the meat into bite-size pieces and return to the pot along with the diced carrots and celery.
Cover and simmer 10 to 15 minutes until carrots are tender.
Optional: Boil the noodles and strain when ready. Separate into bowls.
Scoop portions of the soup into the bowls and garnish with green onion. It's ready to serve!