Make the classic chocolate cake layers:
Preheat the oven to 325 degrees F. Butter three 8-inch round cake pans, line the bottoms with parchment paper, and butter the parchment. Dust with flour, and knock out the excess flour.
In a medium bowl, combine the cocoa powder, hot water, and sour cream and set aside to cool.
Sift the flour, baking powder, baking soda, and salt together into a medium bowl and set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and shortening on medium speed until ribbonlike, about 5 minutes. Add the sugars and beat until light and fluffy, about 5 minutes. Add the eggs, one at a time, beating well after each addition, then add the vanilla and beat until incorporated. Scrape down the bowl and mix again for 30 seconds.
Add the flour mixture, alternating with the cocoa mixture, in three additions, beginning and ending with the flour mixture.
Divide the batter among the prepared pans and smooth the tops. Bake for 35 to 40 minutes, rotating the pans halfway through the baking time, until a toothpick inserted in the center of each cake comes out clean. Transfer the cakes to a wire rack and let cool for 20 minutes. Invert the cakes onto the rack, remove the pans, and let cool completely. Remove the parchment.
Make the salted caramel:
In a small saucepan, combine the cream and fleur de sel. Bring to a simmer over very low heat until the salt is dissolved.
Meanwhile, keeping a close eye on the cream mixture so it doesn't burn, in a medium saucepan combine 1/4 cup water, the sugar, and corn syrup, stirring them together carefully so you don't splash the sides of the pan. Cook over high heat until an instant-read thermometer reads 350 degrees F., 6 to 8 minutes. Remove from the heat and let cool for 1 minute.
Add the cream mixture to the sugar mixture. Whisk in the sour cream. Let the caramel cool to room temperature, then transfer to an airtight container and refrigerate until you are ready to assemble the cake.
Assemble the cake:
Place one cake layer on a serving platter. Spread 1/4 cup of the caramel over the top. Let the caramel soak into the cake, then spread 3/4 cup of the ganache frosting over the caramel. Sprinkle 1 teaspoon of the fleur de sel over the frosting, then top with the second cake layer. Spread with caramel frosting and sprinkle with 1 teaspoon of the fleur de sel. Then top with the third layer. Spread with caramel. Crumb coat the cake and put the cake in the refrigerator for 15 minutes to firm up the frosting. Frost the sides and top with the remaining frosting. Garnish with a sprinkle of fleur de sel.
This cake will keep beautifully in a cake saver at room temperature (cool and humidity free) for up to 3 days. If your room is not cool, place the cake in a cake saver and refrigerate for up to 3 days. Remove the cake from the refrigerator and let it sit at room temperature for at least 2 hours before serving.
*Baked Note: Fleur de sel, or sea salt, is readily available at grocery stores; however, there is a whole world of specialty salts now available online and at specialty food markets. Gray salt (sel gris), Hawaiian sea salt, Italian sea salt, and smoked sea salt will all work well in this recipe, though with slightly different (but always delicious) results.
Make the whipped caramel ganache frosting:
Put the chocolate in a large heatproof bowl and set aside.
In a small saucepan, bring the cream to a simmer over very low heat.
Meanwhile, keeping a close eye on the cream so it doesn't burn, in a medium saucepan combine 1/4 cup water, the sugar, and corn syrup, stirring them together carefully so you don't splash the sides of the pan. Cook over high heat until an instant-read thermometer reads 350 degrees F., 6 to 8 minutes. Remove from the heat and let the caramel cool for 1 minute.
Add the cream to the caramel and stir to combine. Stir slowly for 2 minutes, then pour the caramel over the chocolate. Let the caramel and chocolate sit for 1 minute, then, starting in the center of the bowl, and working your way out to the edges, slowly stir the chocolate and caramel mixture in a circle until the chocolate is completely melted. Let the mixture cool, then transfer it to the bowl of an electric mixer fitted with the paddle attachment.
Mix on low speed until the bowl feels cool to the touch. Increase the speed to medium-high and gradually add the butter, beating until thoroughly incorporated. Scrape down the bowl and beat on high speed until the mixture is fluffy.