Trim the beef of any sinew then slice as thinly as possible (helps if it's partially frozen). Place in a bowl and add the grated ginger, garlic, some pepper, and the sesame oil. Toss to mix, cover and leave to marinate in the fridge for 30-40 minutes.
For the broth - pour the stock into a large pan and add the sliced ginger, star anise, cloves, cinnamon sticks, cardamom, caster sugar, and fish sauce. Bring to the boil, lower the heat, and simmer for 30 minutes.
Add the rice noodles to a large pan of boiling salted water and cook according to packet instructions until tender but still retaining a bite. Drain in a colander and immediately toss with a little sesame oil to prevent them sticking.
Bring the broth to the boil and tip in the beef and bean sprouts, simmer for just 30 seconds then remove from the heat.
Divide the noodles among warm bowls and ladle the hot broth over them, dividing the beef and bean sprouts equally. Scatter over the spring onions, coriander and mint, then serve immediately with lime wedges.