In a large saucepan, heat one tablespoon of coconut oil over medium heat. Add shallots, and stir, cooking just until fragrant. About 1-2 minutes.
Add bell peppers, mushrooms, curry paste, ginger, chicken broth, brown sugar, and fish sauce and bring to a boil. Reduce to simmer. Cover and cook until hot and bubbly, about 8 minutes.
Add coconut milk and return to a simmer. Add shrimp and cook just until pink and cooked through, about 3-5 minutes.
Remove from heat and add sliced green onions, lime juice and fresh basil.