Triple-Chocolate Peppermint Trifle

For the Cake 

Vegetable oil cooking spray 
1/2 cup whole milk 
2 tablespoons unsalted butter 
3/4 cup all-purpose flour 
1/4 cup unsweetened Dutch-process cocoa powder 
1 1/2 teaspoons baking powder 
1/2 teaspoon salt 
2 large eggs, room temperature 
3/4 cup granulated sugar 
1 1/2 teaspoons pure vanilla extract 

For the Syrup 

1/4 cup granulated sugar 
1/3 cup chocolate-flavored liqueur, such as Godiva 

For the Mousse 

2 1/2 cups heavy cream 
12 ounces white chocolate, finely chopped 
1/2 cup coarsely chopped peppermint candies or candy canes 

For the Pudding 

8 ounces milk chocolate, finely chopped 
2 cups heavy cream 
3 large egg yolks, room temperature 

For Serving 

1 1/2 cups heavy cream 
1/4 cup confectioners' sugar 
1/4 cup coarsely chopped peppermint candies or candy canes

1. Preheat oven to 350 degrees. Make the cake: Coat a 9-inch round cake pan with cooking spray. Line bottom with parchment paper; coat with cooking spray. 
2. Bring milk and butter almost to a boil in a small saucepan. Remove from heat, and set aside. Whisk flour, cocoa, baking powder, and salt in a bowl. Put eggs into the bowl of an electric mixer fitted with the whisk attachment. Beat on high speed until pale and fluffy. Gradually add sugar, beating until pale and thick, about 5 minutes. Add vanilla. Reduce speed to low. Add hot milk mixture in a slow, steady stream. Add flour mixture, and beat until just combined. 
3. Pour batter into pan. Bake until center springs back when lightly touched, 25 to 30 minutes. Let cool in pan on a wire rack 20 minutes. Turn out onto rack. Remove parchment; let cool completely. Halve cake horizontally. 
4. Make the syrup: Bring sugar and 1/4 cup water to a boil in a small saucepan, stirring until sugar has dissolved. Let cool completely. Stir in liqueur. 
5. Make the mousse: Prepare an ice-water bath; set aside. Bring 1 cup cream just to a boil in a small saucepan. Place white chocolate in a food processor; with machine running, pour in hot cream in a slow, steady stream, and process until smooth. Transfer to a medium bowl set in ice-water bath. Let cool, stirring occasionally, until thick enough to hold ribbons on surface, about 15 minutes. 
6. Beat remaining 1 1/2 cups cream to nearly stiff peaks. Fold into chocolate mixture, then fold in candies. Cover with plastic wrap, and refrigerate until thickened and almost firm, 4 to 6 hours. 
7. Make the pudding: Put chocolate into a large bowl; set aside. Bring cream almost to a boil in a small saucepan. Whisk yolks in a bowl. Pour in hot cream in a slow, steady stream, whisking. 
8. Pour mixture back into pan. Cook over medium heat, stirring, until thick enough to coat the back of a spoon, about 1 minute. Pour through a fine sieve over chocolate; whisk until smooth. Set bowl in ice-water bath. Let cool, stirring occasionally, until thick enough to hold ribbons on surface, about 15 minutes. Place plastic wrap directly on surface; refrigerate until set, about 3 hours. 
9. To assemble: Spread one-third of the mousse into bottom of a glass trifle bowl that is 8 to 10 inches in diameter. Top with a cake layer, and brush with half the syrup. Top with half the pudding, then another third of mousse. Place remaining cake layer on top; brush with remaining syrup. Top with remaining pudding, then mousse. Cover with plastic wrap, and refrigerate 12 hours. 
10. Beat cream and sugar until soft peaks form. Top trifle with the whipped cream, and sprinkle with candies.