Preheat oven to 325F (160C).

Combine heavy cream, milk, vanilla bean (split and scraped), and cinnamon sticks (if using) in a saucepan.

Bring mixture to a boil over medium heat.

Remove from heat and cover with plastic wrap.

Let steep for 30 minutes to infuse flavors.

Cut brioche bread into 1/4-inch thick slices.

Cut slices into quarters, reserving the rounded top pieces.

Fill a 9x12-inch gratin dish with the quartered bread pieces.

Return milk mixture to a boil, then remove from heat.

Discard vanilla pod and cinnamon sticks.

Add chopped bittersweet chocolate to the milk mixture.

Whisk until the chocolate is melted and smooth.

In a large bowl, combine egg yolks and sugar.

Whisk egg yolks and sugar until well combined.

Slowly pour the chocolate mixture into the egg yolk mixture, whisking constantly to temper the eggs.

Pour half of the chocolate custard over the bread in the gratin dish, ensuring all bread is soaked.

Arrange the reserved bread pieces on top in a decorative pattern.

Press firmly so that the bottom layer of bread absorbs the chocolate mixture.

Spoon the remaining custard over the bread until completely covered and all cracks are filled.

Cover the dish with plastic wrap and press down to soak the bread thoroughly.

Remove the plastic wrap and wipe the edges of the dish with a damp towel.

Let sit for 30 minutes.

Place the gratin dish in a larger pan and fill the outer pan with hot water halfway up the sides of the gratin dish (creating a water bath).

Bake in the preheated oven for about 35 minutes, or until set.

Cool on a wire rack for 15 minutes.

Whisk the creme fraiche until soft peaks form.

Serve the bread pudding warm, garnished with whipped creme fraiche and chocolate shavings.