Pat cod dry, then season all over with 1/2 tsp salt and the black pepper.
Warm the olive oil in a wide skillet over medium heat.
Sauté shallots until translucent, 2–3 minutes. Stir in garlic, ginger, and red pepper flakes; cook 30 seconds.
Add bell pepper and cook until slightly softened, about 2 minutes.
Pour in coconut milk and broth. Stir in lime juice, zest, fish sauce, brown sugar, and remaining salt; bring to a gentle simmer.
Nestle cod into the sauce in a single layer. Cover and simmer gently until opaque and flaky, 6–8 minutes.
Taste the broth and adjust with more lime or salt if needed.
Scatter cilantro over the fish and serve, spooning plenty of sauce over each portion.