Place Dutch oven or stock pot over medium heat. Add oil. Once hot, add chicken and season with salt and pepper. Cook until done. Remove and set aside.
Add onion and pepper to same hot pot. Cook until softened, about 5 minutes. Add garlic and cook until fragrant. Add in curry paste and ginger and stir together. Cook for 5 minutes. The bottom of the pan will probably start to brown. That's okay!
Add in 2 cups of chicken broth. Scrape off the browned bits from the bottom of the pan. Add rest of the chicken broth and coconut milk. Bring mixture to a boil. While waiting for it to boil, chop the cooked chicken and add to the soup. Once the soup is boiling, reduce to simmer. Simmer for 10 minutes.
Add fish sauce, brown sugar, and rice noodles. Let noodles soften in the hot broth for about 5 minutes. Remove from heat and add in chopped green onions, cilantro, and fresh lime juice. Taste and season, if necessary. Serve immediately.