Make the rice. Heat the oil in a small saucepan over medium heat and add the onions, garlic, and carrots. Cook gently, stirring often, until tender but not browned, about 5 minutes. All the rice and cook, stirring frequently, for about 3 minutes, or until the rice is lightly toasted. Add 4 cups of chicken stock and the salt, and bring to a boil, then reduce the heat to low, and simmer for 25 minutes, or until the rice is tender. Remove from the heat and purée in a food processor fitted with the steel blade until fairly smooth, about 1 minute. Add up to 2 ¼ cups more chicken stock as needed to create a thick suce consistency. Return the sauce to the pan, cover, and reserve warm.
Prepare the fish. Season the fish fillets with the salt and pepper, distributing it evenly on both sides. Dip them in the beaten eggs, then lightly flour, and transfer to a medium baking sheet.
Toss the peppers with the fine sea salt and reserve. Place all but 2 tablespoons of the oil in a large wide saucepan or skillet and insert a thermometer. Bring to 113°F over very low heat.
Heat 1 tablespoon of the remaining oil in a separate large heavy sauté pan over medium-high heat and sear the fish in batches of four on both sides, about 2 minutes per side. Use paper towels to wipe out the skillet between batches. Transfer the first of four fillets to the oil and allow to finish cooking for 4 or 5 more minutes, or until the fish is completely opaque throughout. Repeat with the remaining fillets, but remove the first batch from the warm oil and use a slotted spoon to transfer to plates before adding the second batch to the oil.
Spoon ¾ cup of the cream of rice soup onto each plate. Divide the peppers between the plates and place the fish fillets on top of them. Sprinkle with a pinch of Maldon salt and serve.