Line a rimmed baking sheet with a silicone mat. Combine 113 g butter, 150 g sugar, water, corn syrup, and 1 g salt in a heavy saucepan. Cook over medium heat, stirring gently until the butter melts and the mixture becomes uniform. Stop stirring once it boils, attach a candy thermometer, and cook until deep amber and 150°C, about 8 to 12 minutes. Remove from the heat, carefully stir in 5 g vanilla, and immediately spread the bubbling candy into a thin, even layer.

Let the toffee stand for 3 minutes, then scatter 85 g finely chopped semisweet chocolate evenly over the hot surface. Wait 2 minutes for the chocolate to soften, spread it into a thin coating, and leave the slab at room temperature until completely firm, about 45 minutes. Break it into pieces, reserving several attractive shards for decorating. Place the remainder in a sturdy food-safe bag and crush it with a rolling pin, keeping most pieces between coarse crumbs and 6 mm nuggets.

Position an oven rack in the center and heat the oven to 175°C. Grease three 8-inch round cake pans, line each base with parchment, then lightly grease the parchment. Set the pans on a digital scale and have a flexible spatula ready for dividing the batter. Properly lined pans release this tender cake without tearing, while equal batter weights help the three layers bake at the same rate and produce a straight, stable stack.

In a large bowl, whisk the flour, 400 g sugar, 75 g cocoa, baking powder, baking soda, and 5 g salt for 30 seconds, breaking apart any cocoa pockets. In a second bowl, whisk the eggs until uniform, then add the buttermilk, oil, and 10 g vanilla. Whisk until glossy and fully emulsified, with no separate streaks of egg white or oil. Combining each mixture thoroughly now prevents overmixing after the flour becomes wet.

Pour the liquid mixture into the dry ingredients and whisk slowly from the center outward until only a few fine flour streaks remain. Gradually stream in the hot coffee while whisking gently, then scrape the bowl and mix just until the batter is smooth and fluid. Do not continue beating once uniform. Divide approximately 610 g batter among each prepared pan, checking the pan weights for consistency, and tap each pan once on the counter to release large trapped air bubbles.

Bake all three pans on the center rack for 27 to 33 minutes, rotating their positions after 22 minutes if the oven browns unevenly. The layers are done when the centers spring back lightly, the edges begin pulling from the pans, and a tester shows moist crumbs but no wet batter. Cool in the pans for 15 minutes. Run a thin spatula around the edges, invert onto wire racks, remove the parchment, and cool completely for at least 75 minutes before leveling or frosting.

Beat the softened 454 g butter with a paddle attachment on medium speed for 3 minutes, scraping the bowl once, until smooth and slightly aerated. On low speed, add the sifted confectioners’ sugar and 75 g cocoa in four additions, alternating with about 120 g cream. Add the melted cooled chocolate, 10 g vanilla, and 3 g salt, then beat on medium-low for 2 minutes. Add the remaining cream gradually until the frosting holds soft peaks and spreads without tearing cake crumbs.

Level any domed cake tops with a serrated knife. Place one layer cut-side up on a cake board and spread with 180 g buttercream. Pipe a buttercream border around the edge, then scatter about one-third of the crushed toffee inside it. Repeat with the second layer and position the final layer cut-side down. Check the stack from several angles, adjusting before the filling firms. Apply a thin crumb coat over the top and sides, then refrigerate uncovered for 30 minutes.

Cover the chilled cake with the remaining buttercream, using an offset spatula and turntable to smooth the top and sides. Press the remaining crushed toffee around the lower edge and arrange the reserved shards on top, inserting them only far enough to stand securely. Chill the finished cake for 30 minutes to set the decoration. Before serving, let it stand at room temperature for 30 to 45 minutes, then cut 16 slices with a warm, dry knife, wiping the blade between cuts.