Heat the vegetable oil in a large pot over medium heat.
Add the chopped onion and sauté for about 5 minutes until softened.
Stir in the minced garlic and grated ginger, cooking for another 1-2 minutes until fragrant.
Add the red curry paste and cook for an additional minute, stirring to combine.
Pour in the chicken broth and coconut milk, and bring the mixture to a gentle simmer.
Add the shredded chicken, sliced red bell pepper, and mushrooms. Simmer for about 10 minutes.
Stir in the fish sauce, brown sugar, and lime juice. Adjust seasoning to taste.
Add the fresh spinach just before serving, allowing it to wilt in the hot soup.
Ladle the soup into bowls, and garnish with fresh cilantro, sliced green onions, and a lime wedge.