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1
Peel each cardoon stalk with a vegetable peeler or paring knife, removing all stringy outer fibres until only pale, tender flesh remains. Cut into 5 cm lengths and rub each piece immediately with the cut face of a lemon half to prevent oxidation.
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2
Whisk the flour into the cold water in a large pot to form the blanc; add the lemon juice and salt. Bring to the boil, add the cardoon pieces, and cook at a steady simmer for 30 to 45 minutes. The cardoons are ready when a knife passes through the flesh without resistance — they must be fully tender here, as they will not soften further in the gratin.
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3
While the cardoons cook, poach the marrow bones in well-salted simmering water for 15 minutes. Lift out and press the marrow from each bone in one piece. Set aside.
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4
Melt the butter in a heavy saucepan over medium heat. Add the flour and stir constantly for 1 to 2 minutes until the roux is smooth and smells faintly of biscuit but has taken no colour. Add the warmed milk in a steady stream, whisking without pause. Cook, stirring, until the sauce coats the back of a spoon and a drawn finger leaves a clean line. Remove from the heat and stir in the 100 g of Gruyère until fully melted. The Mornay must remain fluid — a sauce stiff enough to hold a peak will make the finished gratin stodgy; this is where the dish lives or dies.
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5
Heat the oven to 200 °C. Drain the cardoons thoroughly. Arrange half the cardoons in an even layer in a buttered gratin dish. Spoon over half the Mornay. Slice the extracted marrow and distribute it across this layer. Add the remaining cardoons, then pour over the rest of the Mornay so that all surfaces are coated.
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6
Scatter the remaining 50 g of Gruyère evenly over the surface, then distribute the breadcrumbs on top. Bake at 200 °C for 20 to 25 minutes. The gratin is done when the surface is deep golden and bubbling actively at the edges, and the kitchen carries the smell of browned cheese.