Heat coconut oil in a large pot or Dutch oven over medium-high heat. Add chicken pieces and cook until lightly browned on all sides. Remove chicken from the pot and set aside.

Add chopped onion to the pot and cook until softened, about 3-4 minutes. Add minced garlic and grated ginger, and cook for another minute until fragrant.

Stir in the red curry paste and cook for 1-2 minutes, stirring constantly, until fragrant and slightly darker in color.

Pour in the coconut milk and chicken broth, whisking to combine and scrape up any browned bits from the bottom of the pot. Bring to a gentle simmer.

Return the cooked chicken to the pot. Add sliced red bell pepper, mushrooms, and snap peas (or green beans). Simmer for 10-15 minutes, or until chicken is cooked through and vegetables are tender-crisp.

Stir in the fish sauce, palm sugar, and lime juice. Taste and adjust seasoning as needed.

Ladle the soup into bowls and garnish with fresh cilantro, Thai basil leaves, and sliced red chilies if desired. Serve immediately with lime wedges on the side.