Heat the olive oil in a large pot over medium heat. Add the onion, garlic, and ginger. Cook for 3 minutes until the onion softens.
Stir in the Thai red curry paste and cook for 1 minute to release the flavors.
Pour in the chicken broth and coconut milk. Bring the mixture to a gentle simmer.
Add the red bell pepper and carrots. Simmer for 8 minutes until the vegetables start to soften.
Stir in the shredded rotisserie chicken and heat through for 3 minutes.
Remove the pot from the heat. Add the fish sauce and lime juice. Stir to combine.
Ladle the soup into bowls and top with cilantro and green onions before serving.