Cook the noodles according to the packet instructions, then drain and set aside to cool slightly, reserving the seasoning packet.
Meanwhile, grate the zucchini and carrot, then squeeze out any excess moisture using a clean tea towel or paper towel.
In a bowl, whisk together the beaten egg, water, plain flour, and the contents of the seasoning packet.
Add the cooked noodles, grated vegetables, and spring onions, stirring until well combined.
Heat 2 tablespoons of vegetable oil in a non-stick frying pan over medium heat.
Add half of the noodle mixture, pressing it down gently to form a pancake.
Cook for 3–4 minutes on each side or until golden and crispy around the edges.
Repeat with the remaining mixture.
Transfer pancake to a serving dish, top with a fried egg and drizzle with sweet soy sauce.
Garnish with extra spring onions and fried shallots.
