Heat coconut oil in a large stockpot or Dutch oven over medium heat. Add bell peppers and onion, cooking with occasional stirring until just tender, about 3 to 4 minutes.

Stir in red curry paste, ginger, and garlic until fragrant, about 1 minute.

Gradually whisk in chicken stock, tomato sauce, fish sauce, and brown sugar. Bring to a boil, then reduce heat and simmer until flavors meld, about 10 to 15 minutes.

Stir in coconut milk and simmer until slightly reduced and thickened, about 10 minutes.

Add shrimp and cook, stirring occasionally, until pink and cooked through, about 3 to 4 minutes. Remove from heat and stir in Thai basil, cilantro, and lime juice. Serve immediately.