Preheat oven to 350 degrees F. Grease and flour 2 (9-inch) round cake pans. Cut rounds of parchment paper to fit into bottoms of pans and place inside.

Set up stand mixer.

In a medium bowl, sift together flour, baking soda, baking powder, and salt. Set aside.

Combine granulated sugar and water in a medium saucepan and place over high heat. Bring to a boil and cook for 2 minutes, stirring frequently.

Transfer sugar syrup from saucepan to bowl of stand mixer. Add chopped chocolate and butter. Allow to stand for about 15 minutes, until the temperature has lowered to 150 degrees F, stirring occasionally. Stir in vanilla.

Add eggs to the mixture in the bowl and beat for about 10 seconds on medium speed.

Keeping beaters on medium speed, add flour mixture to chocolate base and beat for about 2 minutes, scraping down the sides of the bowl as needed.

Divide the batter evenly between the two cake pans. Bake for about 22 minutes, or until a toothpick inserted into the center of each cake comes out clean.

Cool cakes in their pans on a wire rack for 25 minutes, then remove from pans. Remove the parchment paper. Allow cake layers to cool an additional hour before frosting.

Combine the sugar and cream in a medium saucepan and bring to a boil over medium heat, stirring every now and then. Once the mixture has come to a boil, reduce the heat to low and cook on simmer for about 6 minutes, until the liquid reduces a bit.

Pour the hot mixture into a medium bowl and add the butter, chocolate, vanilla extract, and salt. Let this mixture stand for about 10 minutes, stirring occasionally, until all the components have melted.

Set the medium bowl of frosting inside a larger bowl that is filled with water and ice cubes. Use a hand-held mixer to beat the frosting on medium speed, scraping the sides thoroughly from time to time with a rubber spatula. Beat until the mixture thickens and becomes glossy, 6-10 minutes (mine took 10).

Remove the frosting bowl from the ice water bowl and frost the cake layers right away.