In a Dutch oven, over high heat, melt the butter with the shallots, garlic, ginger, basil leaves, and curry paste. Cook until the curry paste has thickened, about 5 minutes, stirring frequently.
Add the chicken and bell pepper, and toss in the curry. Pour over the broth, cover, and simmer 15 minutes, until the chicken is cooked through. Shred the chicken in the pot.
Add the coconut milk. Cook for another 5 minutes, or until warmed through and gently simmering.
Cook the noodles according to package directions.
Divide the noodles between bowls and ladle the soup over. Top as desired with extra coconut milk and cilantro.