Heat the olive oil in a large pot over medium heat. Add the diced chicken thighs and season with salt and pepper. Cook until browned, about 5-7 minutes. Remove the chicken from the pot and set aside.
In the same pot, add the chopped onion, garlic, and ginger. Sauté for 3-4 minutes until fragrant and the onion is translucent.
Add the diced red bell pepper to the pot. Cook for an additional 2 minutes, stirring occasionally.
Pour in the can of coconut milk and chicken broth, stirring to combine. Bring the mixture to a gentle simmer.
Return the cooked chicken to the pot. Add the fish sauce, lime juice, and brown sugar. Stir well and let the soup simmer for about 10 minutes.
Just before serving, stir in the baby spinach until wilted, about 1-2 minutes.
Taste and adjust seasoning with more salt, pepper, or lime juice as desired.
Ladle the soup into bowls and garnish with fresh cilantro and lime wedges on the side.