Preheat oven to 180°C. Roast oxtail on a lined oven tray until golden brown, about 1½ hours, turning after about 45 minutes.
Heat oil in a small saucepan and deep-fry onion and carrot, stirring often until golden, about 6-8 minutes. Do not let vegetables get too dark or the stock will be bitter. Drain on paper towel.
Put konbu and 2 litres of water in a large pot and heat to make a stock. Just before boiling point, add ½ cup cold water and remove konbu. Bring stock back to the boil on a low heat. When almost boiling, add bonito flakes, remove from heat and allow bonito to sink to the bottom of the stock. Strain through muslin.
Put roast oxtail, carrot and onion into a pot with stock and simmer for 4 hours. Remove oxtail, strain stock through muslin and set aside. Remove meat from bones and chop.
For the wontons, heat oil in a frying pan until hot. Fry garlic and ginger until fragrant, then add mushrooms and cook until they wilt. Add wine, sugar, and soy, then transfer to a bowl and mix in water chestnuts and oxtail meat. Check seasoning.
Put 1 tbsp of mixture in the centre of each wonton wrapper. Brush 2 edges of lightly with flour-and-water paste. Fold in half to enclose and seal edges.
Reheat broth and skim off impurities. Blanch wontons in gently boiling water and share among four large bowls. Pour over broth and garnish with spring onions, a few mint leaves and chilli oil to taste.