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1
Soak the scraped vanilla seeds in the rum for at least ten minutes. Combine the sifted flour and sugar in a wide bowl. Add the cold cubed butter and work it into the flour and sugar with cool fingertips, pressing and releasing until the mixture resembles coarse, damp sand with no visible lumps of butter remaining.
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2
Add four egg yolks and the rum-soaked vanilla seeds to the sandy mixture. Fold and press with the fingertips until a cohesive, heavy dough forms. Stop the moment it holds together — prolonged working develops gluten and destroys the dense, fudgy character the dish lives or dies on.
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3
Butter a 22–24 cm round cake mold thoroughly. Transfer the dough and press it by hand to an even depth of 3–4 cm. Do not roll. The surface should be flat and level, with no cracks at the edge.
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4
Beat the reserved egg yolk with a few drops of water and brush it evenly over the surface. Score a crosshatch pattern across the entire top with the tines of a fork, pressing lightly so the lines are defined but do not cut through the dough.
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5
Bake at 170 °C for 40–45 minutes. The gâteau is done when the surface is deeply burnished gold — not pale, not dark brown — and the center yields the faintest resistance when pressed very gently: just barely set, not liquid, not firm.
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6
Remove from the oven and leave the gâteau in its mold on a wire rack until completely cold. The center will firm and become fudgy as the butter recrystallizes during cooling. Do not unmold or slice while warm.