Cook the noodles in boiling water for 3 minutes, or until just tender, then drain and refresh under cold water. Drain again, toss in a little oil and put to one side.
Drain the tofu well, then pat dry with kitchen paper and chop into 2cm chunks.
Trim and chop the mushrooms in half or into quarters through the stalks. Halve, deseed and finely slice the pepper and chilli, trim and finely slice the spring onions. Peel and finely slice the garlic then peel and finely chop the ginger. Drain the water chestnuts.
Squeeze the lime juice into a small bowl, mix in the soy, then pick and tear in most of the coriander leaves.
Heat a splash of oil in a large non-stick frying pan over a medium heat, add the tofu and mushrooms, spreading them out in a single layer, then fry for a few minutes, or until the tofu is golden all over and mushrooms are juicy, turning occasionally.
Scatter over the sesame seeds and toast in the pan with the mushrooms and tofu for 1 minute, then tip out onto a plate and keep warm until needed.
Quickly wipe the pan with a ball of kitchen paper, place back on the heat and turn it up to high. Drizzle in a splash more oil, then add the garlic, ginger, chilli and spring onions and fry for 30 seconds, then add the peppers and water chestnuts, and stir-fry until just starting to soften.
Add the noodles and cook until hot through, stirring regularly. Turn off the heat and stir through half the soy and lime dressing.
Divide the stir-fry between your plates, spoon over the tofu and mushrooms. then drizzle over the remaining dressing. Pick and tear over the remaining coriander, then serve.