Caramel Ganache:
Combine milk chocolate and semi-sweet chocolate in a medium bowl.
Combine sugar, 2 tablespoons of water, and cinnamon stick in a saucepan over medium heat, stirring until sugar is dissolved.
Increase heat and boil without stirring until syrup turns deep orange, about 6 minutes.
Add cream and salt.
Bring mixture to a boil, whisking, until smooth and caramel is dissolved.
Discard cinnamon stick.
Pour hot caramel over chocolate and whisk until chocolate is melted and mixture is smooth. Let cool, whisking occasionally, until completely cooled, about 1 hour.

Using an electric mixer, beat butter in a large bowl until light and fluffy.
Add chocolate mixture in 4 parts, beating continuously with electric mixer. Cover and refrigerate ganache overnight.

Cake:
Preheat oven to 350 F (180 C).
Butter and flour a 9″ x 13″ (23 cm x 33 cm) rectangular mold.
Sift flour, baking powder, and salt into a medium bowl.
Using an electric mixer, beat butter in a large bowl until light and fluffy. Add 1 cup (180 g) of brown sugar, then egg yolks and vanilla.
Add chestnut cream, then milk.
Sift dry ingredients and add to mixture.
Beat egg whites in another large bowl until soft peaks form.
Add remaining brown sugar and beat until stiff but not dry.
Fold egg whites into batter in 3 parts.

Pour batter into prepared mold and bake until cake is golden and a toothpick inserted in the center comes out clean, about 30 minutes.
Let cool completely in mold on a wire rack.

Syrup:
Heat brandy and brown sugar in a small saucepan until sugar is dissolved.

Unmold cake onto a cutting board.
Cut cake into 3 equal parts lengthwise: this will give 3 rectangles of 9″ (23 cm) long and 4″ (12 cm) wide.

On a rectangular plate, place a cake rectangle.
Moisten with half of the brandy syrup.
Spread 1 cup (250 ml) of caramel ganache.
Sprinkle with half of the Brazil nuts.
Repeat once and finish with a cake rectangle.
With remaining ganache, glaze top and sides of cake.
Refrigerate cake while preparing glaze.

Glaze:
Bring cream, sugar, and water to a boil, whisking, until sugar is dissolved. Add chocolate and whisk until chocolate is melted and mixture is smooth.
Let cool until thick but still pourable, about 4 hours.

Pour glaze over top of cake, spreading evenly over sides.
Refrigerate until glaze is set.
Decorate with remaining chestnut cream (if you haven’t eaten it all with a spoon).

Let cake rest at room temperature for at least 4 hours and up to 8 hours.
Serve cake at room temperature.