Lightly coat an 8" round cake pan with oil, and line with plastic, leaving a 4" overhang.

Finely grind chestnuts in a food processor.

Heat ground chestnuts, milk, 3 tablespoons sugar, and salt in a medium saucepan over medium-high heat, stirring occasionally, until bubbles form at edge.

Whisk together yolks, cornstarch, and the remaining 2 tablespoons of sugar in a medium heat-proof bowl.

Slowly add hot chestnut mixture to yolk mixture, whisking constantly. Return to pan; cook over medium-low heat, whisking constantly, until thick, about 2 minutes.

Transfer to the bowl of a mixer. Add vanilla and butter.

Beat on medium speed until cool, about 5 minutes. Stir half the chestnut mixture into melted chocolate.

Beat 1 1/4 cups cream until soft peaks form. Using a rubber spatula, gently fold half the whipped cream into the plain chestnut mixture and the other half into the chocolate-chestnut mixture.

Pour chestnut mousse into prepared pan. Cover with 12 chocolate wafers, working in a circular pattern. Top with chocolate-chestnut mousse and remaining 12 chocolate wafers.

Fold plastic overhang over top to cover cake. Refrigerate overnight.

Uncover cake; place a platter on top, flip, and unmold. Remove plastic.

Beat remaining 1/4 cup cream until soft peaks form. Spread on top of cake. Garnish with chocolate shavings.