Finely slice the spring onions, coarsely grate the carrot and finely chop the pepper / capsicum. Finely grate the ginger and crush the garlic.
Cook the noodles according to the instructions on their packet.
In a large frying pan, heat the vegetable oil then add the beef mince and sliced spring onions.
Turn the heat up high and cook stirring for a couple of minutes, breaking the beef mince up with the back of a spoon, then turn down to a medium high heat and cook for 5 minutes, stirring.
Add the crushed garlic and grated ginger, grated carrot and chopped pepper / capsicum and cook on a medium heat for 3 minutes, stirring every so often, until the vegetables are tender and the beef mince is cooked - it should be brown all the way through.
In a small bowl mix the soy sauce with the sesame oil, rice vinegar, hoisin sauce and water.
Drain the noodles and add to the pan with the sauce, stir to coat everything in the sauce then cook for 2 minutes, until the sauce has thickened and coats the noodles, minced beef and vegetables.
Sprinkle with sesame seeds, if using, and serve straight away.