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1
Bring a large pot of water to the boil. Whisk in the flour and the juice of one lemon to form the acidulated blanc. Working quickly, strip every filament of outer fibre from each cardoon stalk with a paring knife as one would string celery, then rub the exposed flesh immediately with the cut lemon. Lower the prepared stalks into the simmering blanc and cook for 30 to 45 minutes. The stalks are done when a knife passes through them without resistance and the flesh is fully tender.
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2
Drain the cardoons and, once cool enough to handle, cut them into 5 cm lengths. This is where the dish lives or dies: any stalk that retains stringy fibre must be peeled again before cutting, or the gratin will be unpleasant throughout. Set the cut pieces aside.
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3
Bring a separate pan of water to exactly 80°C — use a thermometer and maintain the temperature steadily. Submerge the marrow bones and poach for 10 minutes. Remove and allow to cool briefly, then press or tap the marrow free from the bones. It should emerge as quivering, barely set discs that hold their shape. Marrow that has melted into the liquid has been overcooked; marrow that is waxy and opaque has been undercooked.
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4
Make the béchamel: melt the butter in a heavy saucepan over medium heat, add the flour, and stir for one minute to cook out the raw taste. Add the milk in a steady stream, whisking continuously, and cook until the sauce is smooth, glossy, and coats the back of a spoon. Remove from the heat and stir in the 50 g of Gruyère until fully melted. Season with salt. The sauce should flow easily — if it mounds on the spoon, thin it with a little warm milk.
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5
Heat the oven to 200°C. Butter the gratin dish thoroughly. Arrange the cardoon pieces in an even layer across the base. Lay the marrow discs evenly across the cardoons. Pour the enriched béchamel over the entire surface, then scatter the remaining 50 g of Gruyère across the top.
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6
Bake at 200°C for 20 to 25 minutes. The gratin is ready when the surface is deeply golden and the sauce is visibly bubbling at the edges of the dish.