Cut the chilli pepper lengthwise. Remove seeds. Finely dice the pod. Knead butter and chili cubes with a fork. Place on aluminium foil and form into a roll. Leave to set in the freezer.
For the Gremolata limes, wash them hot, rub them dry and peel them into strips with a zest ripper. Finely chop the peel. Squeeze the lime, put the juice aside. Halve the remaining lime and cut into slices.
Peel and finely dice the ginger. Finely chop the coriander (except for a few leaves for garnishing). Peel garlic and chop finely. Mix lime zest, ginger, coriander and garlic. Wash fish inside and out and pat dry.
Season with salt and pepper and sprinkle with lime juice. Score one side of the fish with a knife. Carefully push halved lime slices into the cracks. Place the fish on a baking tray lined with baking paper.
Spread Gremolata on the trout. Cook in the preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for about 20 minutes. Simmer rice in 500 ml boiling salted water for about 20 minutes. Peel, wash and cut carrots into strips.
Cook the carrots in boiling salted water for about 5 minutes, drain and leave to drain. Drain rice and let it drain. Arrange fish, carrots and rice on plates. Cut butter into slices and add.
Garnish with coriander leaves and a chilli pepper.