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1
Melt butter in a heavy sauté pan over medium-low heat. Add the sliced carrots, season lightly, and cook, stirring occasionally, until completely soft and yielding — there must be no resistance when pressed with a spoon. The carrots should be pale gold at the edges but not browned.
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2
Transfer the cooked carrots to a blender and process to a smooth purée. Pass the purée through a fine-mesh sieve, pressing firmly with a ladle to eliminate every fibrous trace. This is where the dish lives or dies: any residual texture will fracture the finished flan and destroy the smooth, trembling cylinder the preparation demands.
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3
In a bowl, combine the sieved purée with the 3 whole eggs, 2 egg yolks, and 200 ml of double cream. Season with salt, white pepper, and nutmeg. Whisk until fully homogenous. Dip a spoon into the mixture, coat the back, then draw a finger across it: the line must hold cleanly and without bleeding.
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4
Butter 6 to 8 dariole moulds or ramekins generously on base and sides. Fill each to three-quarters capacity. Set them in a deep baking dish and pour just-boiled water around them until it reaches halfway up the outside of the moulds.
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5
Bake at 160 °C in the bain-marie for 30 to 35 minutes. The custards are done when a skewer inserted into the centre withdraws clean and the surface shows a gentle, uniform wobble when the dish is tapped — but yields no liquid and no raw tremor at the very heart.
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6
Remove the moulds from the water bath and rest for 5 minutes. Run a thin knife around the inner edge of each mould. Invert onto a warm plate with a single, decisive movement. The flan should release as a smooth, vibrant cylinder — deep orange, self-supporting, trembling gently but holding its form without slumping.