In medium pan, whisk together coconut milk, curry paste, and minced pepper.
Holding ginger over pan, squeeze to extract juice into pan; discard solids. Add lemongrass segments. Cook over medium heat, uncovered, 6 to 8 minutes, until slightly thickened.
Stir in basil, and season with salt and white pepper.
Pour a small amount of sauce into an 8-inch-square baking dish. Arrange fish on sauce, and pour remaining sauce over fish. Cover dish with foil and bake at 400°F until fish is opaque and flaky, 20 to 25 minutes.
Spoon a bit of sauce into the center of four individual plates.
Place a piece of fish on each puddle, and spoon additional sauce on top of each portion of fish.
Garnish with cilantro sprigs and drops of hot chili oil around plate, if desired, and serve immediately.