In a medium saucepan, bring the cream, cinnamon, salt, and 2 tablespoons water to a simmer over medium-high heat. Off the heat, cover and steep for 15 minutes. Meanwhile, put the chocolate in a medium bowl and set a fine strainer over it.

Pour 1/4 cup water into a heavy-duty 3-quart saucepan. Pour the sugar in the center of the pan and pat it down until evenly moistened (there should be clear water all around the sugar). Cover the pan and cook over medium-high heat until the sugar dissolves, 2 to 4 minutes. Uncover and cook without stirring until the syrup begins to color slightly, about 1 minute. Reduce the heat to medium and continue to cook, swirling the pot gently if the syrup colors unevenly.

When the caramel turns reddish amber, 1 to 2 minutes longer, take the pan off the heat and immediately stir in the cream mixture. Simmer over low heat, stirring constantly, until the caramel is completely dissolved, 1 to 3 minutes.

Pour the caramel cream through the strainer onto the chocolate and discard the cinnamon. Whisk until the chocolate melts and the mixture is smooth. Scrape into a wide, shallow bowl, cover loosely, and refrigerate until thoroughly chilled, at least 4 hours and up to 3 days.

Put the chocolate, butter, corn syrup, and salt in a heatproof bowl set in a skillet of barely simmering water. Stir gently until the chocolate melts and the mixture is perfectly smooth. Off the heat, stir in 6 tablespoons cool water. Let cool and thicken at room temperature without stirring for at least 3 hours. The consistency should be like chocolate pudding.

Line the bottoms of three 9x2-inch round cake pans with parchment. Position a rack in the lower third of the oven if the three pans will fit on it. Otherwise, position racks in the upper and lower thirds of the oven. Heat the oven to 350 degrees F.

In a small bowl, whisk the cocoa and 1/2 cup lukewarm water. In a liquid measuring cup, mix the buttermilk with 1/2 cup cool water. In a medium bowl, whisk the flour, baking soda, and salt and sift them three times onto a sheet of parchment.

In a stand mixer fitted with the paddle attachment, beat the butter on medium speed until creamy, about 15 seconds. Add the sugars gradually, beating until the mixture lightens in color and appears sandy but fluffy, about 5 minutes total. Dribble the eggs in a little at a time, taking a full minute to add them. Continue to beat for a few seconds until the mixture is smooth and fluffy.

Stop the mixer and add the cocoa mixture. Beat on medium speed just until combined. Stop the mixer and, using the parchment as a chute, add about one-quarter of the flour. Mix on low speed just until incorporated. Stop the mixer and add one-third of the buttermilk. Mix just until blended. Repeat, stopping the mixer between additions and scraping the bowl as necessary, until the remaining flour and buttermilk are mixed in.

Divide the batter evenly among the pans. Bake until a toothpick inserted in the center of each cake comes out clean, 17 to 20 minutes (if baking on two levels, rotate the upper and lower pans halfway through baking). Cool the cakes on racks for 5 minutes and then turn onto the racks, remove the parchment, and cool completely.

Beat the chilled filling in a stand mixer fitted with the paddle attachment at medium speed until it's very thick and stiff enough to hold a shape but still spreadable, 1 to 2 minutes. Don't over beat. Put a cake layer upside down on a cardboard cake circle or tart pan bottom. Spread half of the filling evenly all the way to the edge of the layer. Top with a second upside-down layer and gently press in place. Spread with the remaining filling. Top with the third layer, again upside down. Smooth any filling protruding from the sides.

With an offset spatula, spread a very thin layer (about 1/2 cup) of frosting evenly over the top and sides of the assembled cake to smooth the surface, glue on crumbs, and fill cracks. (Stirring the frosting more than necessary dulls the finish and makes it set up too hard.) Spread the remaining frosting all over the top and sides of the cake, swirling the surface with the spatula if desired. Top with the chocolate shards (if using) and serve at room temperature.