Fill a 2 bowls halfway with cold water. Add 4-5 ice cubes to each bowl. Take 2 of the scallion greens and cut them into thin slices lengthwise. Place them in one of the ice baths and let them sit for 30 minutes. They will naturally curl over time.
12 scallions
Bring a small saucepan of water up to a boil. Add the remaining scallion greens and turn off the heat. Let them stand for 1 minute before plunging them into the second ice bath. Let them stand for a minute more.
Drain the blanched scallion greens and transfer them to a high-powered blender. Add the lime juice and blitz until very smooth. Pour the purée into a bowl and set it aside until ready to use.
1 lime
Place a heavy-bottom pot over medium heat. Add the oil and heat until shimmering. Add the scallion whites and sauté until just softened. Stir in the garlic and ginger, and sauté for a minute more. Pour in the coconut milk, fish sauce, and sugar. Bring everything up to a simmer and let it cook for 15 minutes.
1 tbsp neutral oil , 4 cloves garlic, 2 tbsp ginger, 2 (400 ml, 13.5 fl oz) cans coconut milk, 3 tbsp fish sauce, 2 tsp raw sugar
While the broth is simmering, bring a large pot of water up to a boil. Add the udon noodles and cook according to the package's directions. Drain the noodles and divide them across four bowls.
1.25 kg (3 lbs) udon noodles
Take the coconut mixture off the heat and transfer it to a blender. Carefully blend the broth until smooth. Pour it back into the pot and add the scallion purée. Stir to combine.
Drain the scallion curls and sprinkle them over the noodles. Finish with toasted sesame seeds, drained scallion curls, and wild violet petals. Serve immediately.
1 tsp toasted sesame seeds, Wild violet petals