Preheat the broiler.
Prepare the noodles according to package directions and set aside.
Place the chiles onto foil and coat with 1 tablespoon of the sesame oil. Close foil loosely and broil until soft, about 10 minutes.
In a pot, bring the broth to a boil. Add the green parts of the scallions and half of the garlic to the broth. Keep at a simmer.
Heat the remaining 3 tablespoons sesame oil in a wok or large cast-iron sauté pan to medium-high heat. Remove the stems of chiles and place into the pan with the remaining garlic, the curry paste, and the white parts of the scallions, basil, and mushrooms. Sauté for 8 to 10 minutes.
Add the noodles and sauté for 3 more minutes, adding soy sauce to taste. Place the contents of the wok into four bowls. Ladle 2 scoops of the broth into each bowl. Garnish with fresh basil leaves and serve.