In a medium saucepan, whisk together the cornstarch, cocoa powder, and granulated sugar.

Gradually add the cold milk while whisking until smooth.

Place over medium heat and cook, stirring constantly, until the mixture comes to a gentle boil and thickens to the consistency of pudding.

Remove from the heat. Transfer to a bowl and press plastic wrap directly onto the surface to prevent a skin from forming. Let cool completely to room temperature.

Beat the softened butter and powdered sugar for 2 to 3 minutes, until light and creamy.

Add the cooled chocolate pudding to the butter mixture a few spoonfuls at a time, beating well after each addition.

Mix in the rum extract and ground walnuts. Set aside until ready to assemble the cake.

Preheat the oven to 350°F (180°C).

Line the bottom of a 9-inch springform pan with parchment paper and lightly grease the pan.

In a small bowl, whisk together the flour, baking powder, and salt.

Place the whole eggs and granulated sugar in a large mixing bowl.

Using an electric mixer, beat on high speed for about 7 to 10 minutes, until the mixture is very pale, thick, and approximately tripled in volume. When the beaters are lifted, the batter should fall back in thick ribbons.

Sift the flour mixture over the eggs in two or three additions. Gently fold with a large spatula after each addition, taking care not to deflate the eggs.

Pour the batter into the prepared pan and gently level the surface.

Bake for 25 to 30 minutes, or until the top springs back lightly when touched and a toothpick inserted into the center comes out clean.

Let the cake cool in the pan for about 10 minutes. Remove it from the pan and cool completely on a wire rack.

Once completely cool, slice the cake horizontally into two even layers.

Combine the water and sugar in a small saucepan.

Bring to a boil and simmer for about 1 minute, just until the sugar has completely dissolved.

Remove from the heat and cool completely.

Stir in the rum extract after the syrup has cooled.

Place the bottom cake layer inside the clean springform ring or on your serving platter.

Brush approximately half of the rum syrup evenly over the cake.

Spread all of the chocolate walnut filling over the cake in an even layer.

Brush the cut side of the second cake layer with the remaining syrup.

Place the second layer over the filling and press very gently to level the cake.

Refrigerate for about 30 minutes to allow the filling to firm before adding the ganache.

Place the chopped milk and dark chocolate in a heatproof bowl.

Heat the heavy cream in a small saucepan until steaming and just beginning to simmer. Do not let it boil vigorously.

Pour the hot cream over the chocolate and let stand for 2 minutes.

Stir gently until the chocolate is completely melted and the ganache is smooth and glossy.

Let the ganache cool for several minutes until it is still pourable but no longer hot.

Pour over the top of the chilled cake and spread gently to the edges.

Refrigerate for at least 1 hour, or until the cake and ganache are well chilled.

Remove the springform ring and transfer the cake to a cake stand or serving platter if necessary.

Beat the cold heavy whipping cream with the powdered sugar until firm peaks form.

Spread a thin but complete layer of whipped cream around the sides only of the cake. This acts as the coating that holds the walnuts in place.

Working over a baking sheet or wide bowl, gently press the walnuts onto the whipped-cream-covered sides of the cake. Rotate the cake as you work and reuse any walnuts that fall onto the tray.

If desired, use any remaining whipped cream to pipe a few rosettes around the top of the cake.

Refrigerate for at least 20 to 30 minutes before slicing.