Place chestnuts, ¾ cup sugar, vanilla bean (seeds and pod) and pinch salt in a large saucepan and cover with water by 2 inches. Bring to a boil, reduce to a simmer and simmer for 45 minutes. Remove from heat and let chestnuts cool in syrup, then drain.

Put rack in center position and heat oven to 350°. Butter a 9½-inch springform pan or deep fluted tart pan with a removable bottom.

Chop chocolate into small pieces. In a metal bowl set over a saucepan of barely simmering water, melt chocolate with remaining ¾ cup sugar and butter, stirring, until smooth. Remove bowl from heat and whisk mixture until cooled to lukewarm, then whisk in egg yolks and flour.

In a clean bowl, beat egg whites until stiff but not dry. Gently fold whites into batter in 2 additions.

Pour batter into prepared pan; gently press chestnuts into top. Bake until top of cake has formed a thin crust, about 45 minutes. Cool cake in pan on rack for 5 minutes, then release from pan and let cool completely.