Heat the coconut oil in a large pot over medium heat. Add the diced onion and cook until softened, about 5 minutes.
Stir in the minced garlic and grated ginger, cooking for an additional 1-2 minutes until fragrant.
Add the Thai red curry paste to the pot and cook for 1-2 minutes, stirring constantly, until the paste is well combined with the onions and garlic.
Pour in the chicken broth and bring to a simmer. Cook for 5 minutes to allow the flavors to meld.
Stir in the coconut milk and return to a simmer.
Add the thinly sliced chicken breasts and cook for 5-7 minutes, or until the chicken is cooked through and tender.
Add the coconut aminos, lime juice, and coconut sugar (if using). Adjust seasoning to taste. If you prefer more tanginess, you can add additional lime juice.
Stir in the sliced mushrooms, shredded cabbage (or bok choy), and red bell pepper (if using). Cook for an additional 3-5 minutes until the vegetables are tender.
Taste and adjust the seasoning with more coconut aminos or lime juice if needed.
Ladle the soup into bowls and garnish with fresh cilantro. Serve with lime wedges on the side.