Prep ingredients. Peel and finely chop the shallots. Peel and grate the garlic and ginger. Blend the coconut milk with the basil until smooth and set aside.
Make broth. Heat half the oil in a large saucepan over a medium-high heat. Add the shallots and ginger and cook for 6-7 mins, until golden.
Add the garlic and cook for another 1 min.
Remove half of the shallot mixture to a small bowl and set aside.
Pour the stock into the pan and bring to a simmer. Turn the heat to low and keep the broth on a gentle simmer, topping up with a splash of water, if needed, while you continue with the rest of the recipe.
Make peanut rāyu. Juice half the lime and cut the other half into wedges. Roughly chop the peanuts. Add the crispy chilli oil, soy sauce and peanuts to the reserved fried shallot mixture. Taste and adjust the seasoning with sugar, salt and the lime juice. Set aside.
Cook broccoli. Heat the remaining 1 tbsp of oil in a medium frying pan over a high heat. Add the broccoli with a pinch of salt and stir-fry for 2-3 mins, until tender and slightly charred in places. Keep warm.
Cook noodles. Meanwhile, cook the noodles following the instructions on the packet, then drain.
Assemble and serve. Divide the coconut basil mixture between your serving bowls, then pour in the hot broth. Add the cooked noodles and top with the charred broccoli. Drizzle generously with the peanut rāyu and sprinkle with sesame seeds. Serve with lime wedges for squeezing over.
