Soak the noodles in a bowl of cold water and let sit for 20 minutes. Then rinse with cold water.
Clean the shallot and finely chop. Peel and grate the ginger. Cut the chili pepper in half, remove the seeds and chop finely. Heat up the oil in a saucepan. Add shallots, chili and ginger and sauté for 3-5 minutes, until fragrant. Add curry paste and cook, stirring, 1 minute. Pour in coconut milk, fish and soy sauce, add sugar. Simmer for 15 minutes until the sauce thickens a little.
Finely chop red cabbage. Break the broccoli into small florets. Cut carrots into thin strips. Peel the onion and cut into feathers.
Heat oil in a wok over high heat. Add onions, carrots and broccoli. Roast for 5 minutes, broccoli should remain bright green. Add noodles and stir in vegetables. Pour in the sauce and heat for 2-3 minutes.
Divide the noodles among bowls, top with red cabbage and sprinkle with sesame seeds. Drizzle with lime juice and garnish with basil leaves.