Peel the carrots and thinly slice them lengthwise using a vegetable peeler. Reserve 4 wide, beautiful strips. Finely julienne the rest. Blanch all together in boiling salted water for 5 minutes, then cool and drain.
Cut the scorpionfish fillets into pieces and pulse in a food processor. Gradually incorporate the egg whites while processing.
Transfer to a bowl, season with salt, white pepper, and nutmeg. Refrigerate for 15 minutes. Place the bowl over ice and fold in the very cold fresh cream (30 cl) gradually, working vigorously with a wooden spoon. Adjust seasoning if needed.
Preheat oven to 180°C (thermostat 6). Line the sides of 4 buttered ramekins with the reserved carrot strips. Fill with the mousseline mixture and cover with parchment paper. Place in a bain-marie with boiling water and bake for 20 minutes.
For the sauce, heat the orange juice with peeled and finely chopped ginger. Whisk in the 100 g butter, then the 100 g cream. Season with salt and pepper, and stir in finely chopped chives.
Unmold the mousselines. Reheat the julienned carrots in boiling water for 1 minute, drain, and use to garnish. Serve surrounded by the ginger sauce.