Preheat oven to 325°F (160°C). Butter three 8-inch round cake pans. Line the bottom of each with parchment paper, and butter the parchment. Dust with flour and knock out the excess.
Combine the cocoa powder, hot water, and sour cream. Set aside to cool.
Sift the flour, baking power, baking soda, and salt together. Set aside.
Using an electric mixer, beat the butter and shortening on medium speed until ribbon-like, about 5 minutes. Add both the sugars and beat until light and fluffy, about 5 minutes. Add the eggs, one at a time, and beat well after each addition. Add the vanilla and mix well. Scrape down the sides of the bowl and mix again for 30 seconds.
Add the flour mixture, alternating with the cocoa mixture, in three portions, beginning and ending with the flour mixture.
Divide the batter evenly among the prepared pans and smooth the tops. Bake 35-40 minutes, rotating the pans halfway through. Cakes are done when a toothpick inserted in the center of each cake comes out clean.
Cool the cakes in the pans for 20 minutes on wire racks. Remove from the pans and let cool completely. Remove the parchment paper.
To 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 has dissolved. Be careful not to let the cream burn.
In a medium saucepan, combine 1/4 cup (60ml) water, sugar, and corn syrup, stirring carefully so as not to splash the sides of the pan. Cook over high heat about 6-8 minutes, until an instant-read thermometer reads 350°F (175°C). Remove from 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 time to assemble the cake.
To make the frosting:
Put the chocolate in a large heatproof bowl and set aside.
Bring the cream to a simmer over very low heat. Make sure the cream does not burn.
In a medium saucepan, combine 1/4 cup (60ml) water, sugar, and corn syrup, stirring carefully so as not to splash the sides of the pan. Cook over high heat for 6-8 minutes until an instant-read thermometer reads 350°F (175°C). Remove from the heat and let the caramel cool for 1 minute.
Add the cream to the caramel. Stir slowly for 2 minutes. Then, pour the caramel over the chocolate. Let sit for 1 minute. Then, starting in the center of the bowl, and working out to the edges, slowly stir in a circle until the chocolate is completely melted. Let cool, then transfer to the bowl of an electric mixer.
Mix on low speed until the bowl feels cool to the touch. Increase speed to medium-high and gradually add the butter, beating until thoroughly incorporated. Scrape down the sides and beat on high speed until the mixture is fluffy.
To assemble the cake:
Place one cake layer on a serving platter. Spread 1/4 cup caramel over the top, letting it soak into the cake. Spread 3/4 cup of ganache frosting over the caramel. Sprinkle 1 teaspoon fleur de sel over the frosting. Top with the second cake layer. Spread with frosting and sprinkle with 1 teaspoon fleur de sel. Top with the third cake layer. Spread with caramel. Crumb coat the cake and put the cake in the refrigerator for 15 minutes.
Frost the sides and top of the chilled cake with the remaining frosting. Garnish with a sprinkle of fleur de sel.
Notes
The cake will keep in an airtight container at room temperature (cool and humidity-free) for up to 3 days. It may instead be refrigerated for up to 3 days. Allow the cake to sit at room temperature for at least 2 hours before serving.
Recipe very slightly adapted from Baked: New Frontiers in Baking.