Prep the pans. Preheat the oven to 325°F (163ºC). Line the bottoms of three 8-inch cake pans with parchment paper and coat the pans with nonstick baking spray.
Bloom the chocolate and cocoa. Place the chopped unsweetened chocolate and cocoa powder(1/4 cup) in a medium heatproof bowl. Pour the hot coffee (3/4 cup) over the top and stir to moisten the cocoa. Let stand for 5 minutes, then stir until smooth. If pieces of chocolate remain, microwave in 15-second intervals, stirring after each, just until completely melted. Set aside to cool slightly.
Combine the dry ingredients. In a large bowl, whisk together the flour (2 1/4 cups), granulated sugar (1 1/2 cups), brown sugar (1/4 cup), baking soda (1 1/2 teaspoons), salt (1 1/2 teaspoons), and baking powder (1 teaspoon) until evenly combined.
Combine the wet ingredients. In a medium bowl, whisk the eggs (2), egg yolk (2), buttermilk (1/2 cup), oil (1/2 cup), mayonnaise, and vanilla (2 teaspoons) until smooth. Add the chocolate mixture and whisk until completely incorporated.
Finish the batter. Pour the wet ingredients into the dry ingredients. Using a spatula, gently fold just until the batter is smooth and no streaks of flour remain. Do not overmix.
Divide and bake. Divide the batter evenly among the prepared pans, about 545 grams per pan, and smooth the tops. Bake for 26–28 minutes, or until the centers have lost their shine and spring back when lightly touched. A toothpick inserted in the center should come out with a few moist crumbs but no liquid batter.
Cool the cake layers. Let the cakes cool in their pans on wire racks for 15 minutes. Run a thin knife around the edges if needed, then carefully turn the layers out onto the racks, remove the parchment, and let them cool completely before frosting.
Melt the chocolate for the frosting. Place the dark chocolate chips (12 ounces) and heavy cream in a microwave-safe bowl. Microwave for 30 seconds and stir thoroughly. Continue microwaving in 15-second intervals, stirring after each, just until the chocolate is completely melted and the mixture is smooth. Set aside until completely cooled to room temperature.
Start the fudge frosting. Using the paddle attachment of a stand mixer, beat the slightly cold butter (2 cups) until light and fluffy, about 4–5 minutes. Sift the cocoa powder (1 1/4 cups) and powdered sugar (2 1/4 cups) into the bowl. Add the corn syrup (1/4 cup) and vanilla (2 teaspoons). Mix on low until the dry ingredients are incorporated, then increase the speed and beat for 2–3 minutes.
Finish the fudge frosting. Add the cooled chocolate-cream mixture and mix on low until incorporated. Scrape down the bowl, then beat on medium-high for 3–5 minutes, until the frosting is smooth and fluffy. Note: If the frosting is too soft, refrigerate it briefly, then beat again. If it's too firm to spread, let it soften slightly at room temperature; if needed, beat in 1 tablespoon heavy cream at a time until spreadable. Assemble and frost the cake. Place one completely cooled cake layer on a serving plate or cake stand. Spread an even layer of fudge frosting over the top. Add the second cake layer and repeat, then top with the final layer. Frost the top and sides of the cake with the remaining frosting. Top with chocolate curls if desired.