In a nonstick saucepan, over medium heat, combine 2 cups of the milk, sugar, and vanilla. Whisk to dissolve the sugar. When the mixture comes to a gentle boil, take 1 cup of the milk-sugar mixture and add it to the yolks. Whisk to blend well. Temper the egg mixture to the milk mixture. Cook over medium heat until it thickens slightly, 4 to 5 minutes, whisking occasionally. Over medium heat, slowly add the cornstarch mixture to the saucepan, whisking constantly for 1 minute. Using a wooden spoon, continue stirring for about 2 minutes. Add the chopped white chocolate and continue stirring for 2 more minutes. Add the butter and stir until it is completely melted and mixture has thickened to a custard, about 2 minutes. Cover with plastic wrap, pressing the wrap down the surface of the custard to prevent a skin from forming. Cool completely, stirring occasionally. Soften the gelatin in the water. In a small saucepan, combine the gelatin and cream. Place over medium heat and cook until the gelatin dissolves, about 1 minute. Remove from the heat. In a large bowl, combine the pastry cream and gelatin. Mix well. Fold 1 1/2 cups of the sweetened cream into the mixture.

Combine the sugar syrup and liqueur together. Brush the tops of the sliced cake with the syrup. Let the syrup soak into the cake for 10 minutes. Line a 9 by 5 by 3-inch loaf pan with plastic wrap, allow the wrap to overhang the pan. Place a piece of cake on the bottom of the pan. Place 1 pint of the raspberries over the cake. Spoon half of the cream mixture over the berries. Place the second piece of cake on top of the cream mixture. Repeat with the remaining berries, chocolate mixture and cake. Cover the top with the overhanging plastic wrap and refrigerate for at least 4 hours. Remove from the refrigerator and invert onto a glass serving platter. Ice the sides and top of the terrine with the remaining 1 1/2 cups of whipped cream. Top the terrine with the shaved chocolate. Spoon the sauce in the center of each plate. Slice the terrine into individual servings. Place each slice in the center of the sauce. Garnish each with a sprig of mint.