Soak rice noodles in warm water for 20 minutes until softened, then drain and set aside.
Heat vegetable oil in a large pot over medium heat.
Add red curry paste and cook for 1 minute until fragrant.
Add chicken, garlic, and ginger; sauté for 3 to 4 minutes until chicken is partially cooked.
Add sliced bell pepper and cook for another 2 minutes.
Pour in chicken broth and coconut milk, stirring to fully incorporate the curry paste.
Bring the soup to a gentle simmer and stir in fish sauce and brown sugar.
Simmer for 5 to 7 minutes to allow flavors to meld.
Add the soaked noodles and baby bok choy to the pot; cook for 2 to 3 minutes until noodles are tender and greens are wilted.
Remove from heat and serve garnished with fresh cilantro and lime wedges.