Heat the coconut oil in a large pot over medium heat. Add the chopped onion and sauté for about 5 minutes, or until it becomes translucent.
Stir in the minced garlic and grated ginger, cooking for an additional minute until fragrant.
Add the red curry paste and cook for 1-2 minutes, stirring continuously to combine the flavors.
Add the chicken pieces to the pot, cooking until they're no longer pink on the outside, about 4-5 minutes.
Pour in the coconut milk and chicken broth, and add the sliced carrots, chopped bell pepper, and snap peas or green beans. Bring the mixture to a gentle simmer.
Stir in the soy sauce or tamari, and let the soup simmer for about 15 minutes, allowing the vegetables to cook and the flavors to meld.
Taste the soup and adjust seasoning with salt, pepper, and lime juice as needed.
Ladle the soup into bowls and garnish with fresh cilantro, if desired. Serve warm.