Heat oven to 350°. Butter a 10-inch springform pan and dust with 2½ tablespoons breadcrumbs.

Place bread in a large bowl. Bring milk just to a simmer; pour over bread and let soak until mostly absorbed, about 1½ hours.

In a heatproof bowl set over a pan of simmering water melt chocolate, stirring until smooth.

In the bowl of an electric mixer fitted with the paddle attachment, beat together sugar and egg yolks on medium-high speed until light and fluffy, about 2 minutes. Add butter and beat to combine. Add bread mixture, chocolate and almond flour; beat until well combined.

In a separate clean bowl, whisk egg whites and pinch salt to soft peaks; gently fold into batter. Pour batter into prepared pan and dust with remaining 2½ tablespoons breadcrumbs. Bake for 1 hour, then reduce oven temperature to 300° and continue baking until tester inserted into center comes out clean, about 50 minutes more.

Transfer cake to rack to cool for 10 minutes. Remove from pan and cool completely. Serve sprinkled with confectioners' sugar and chocolate shavings.