Bring a large pot of water to a boil. Cook the rice vermicelli noodles according to package instructions, then drain and rinse with cold water to stop cooking. Set aside.

In a large soup pot or Dutch oven, heat the vegetable oil over medium-high heat. Add the Thai green curry paste and stir-fry for 1 minute until fragrant.

Add the sliced chicken breast to the pot and cook for 3-4 minutes, stirring frequently, until the chicken is mostly white on the outside.

Pour in the chicken broth and coconut milk. Stir well to combine the paste with the liquids. Bring the mixture to a gentle simmer.

Add the red bell pepper and snap peas. Simmer for 5-7 minutes until the vegetables are tender-crisp and the chicken is fully cooked.

Stir in the fish sauce and brown sugar. Remove the pot from heat and stir in the fresh lime juice.

Divide the cooked noodles into bowls and ladle the hot soup over them. Garnish generously with fresh cilantro or Thai basil before serving.