Make the icing first: The icing needs to cool completely and thicken before assembling the cake, so prepare it first. Combine the butter, chocolate, granulated sugar, heavy cream, and corn syrup in a medium saucepan over medium heat. Stir constantly until the butter and chocolate have melted. Continue to cook, stirring occasionally, as the sugar dissolves and the mixture comes to a full boil. (You should see bubbling in the center of the saucepan, not just around the edges.) Once boiling, cook for 2 minutes, or until the mixture reaches 220°F (104°C). Remove from heat and stir in the vanilla extract. Carefully taste and add a pinch of salt, if desired. Leave uncovered and set aside to cool and thicken for at least 2 hours, or until it reaches a spreadable consistency. This gives you plenty of time to bake and cool the cake layers. See the Make Ahead Tip if preparing in advance. Yields about 2 and 1/4 cups icing.
Preheat oven to 350°F (177°C). Grease three 9-inch cake pans, line with parchment paper rounds, then grease the parchment paper. Parchment paper helps the thin cakes seamlessly release from the pans; they may crack and crumble otherwise. (If it’s helpful, see my parchment paper rounds for cakes video & post. You can also reuse the parchment rounds for each batch or cut 9 individual rounds.) Make the cake batter: Whisk the flour, baking powder, baking soda, and salt together in a large bowl. Set aside. Using a handheld or stand mixer fitted with a paddle attachment, beat the butter and sugar together on high speed until smooth and creamy, about 5 minutes. Scrape down the sides and up the bottom of the bowl with a silicone spatula as needed.
On medium-high speed, add 1 egg at a time, beating well after each addition. Beat in the vanilla extract. Scrape down the sides and up the bottom of the bowl with a silicone spatula as needed.
With the mixer on low speed, add the dry ingredients in three additions alternating with the buttermilk, beginning and ending with the dry ingredients, and mixing each addition just until incorporated. Do not overmix this batter. The batter will be smooth, velvety, and slightly thick.
Bake the layers: You’ll have about 7 cups of batter total, so each of the 9 cake layers will use slightly less than 1 cup of batter, or about 200–210g. Keep any unused batter loosely covered at room temperature while the other layers bake. Pour slightly less than 1 cup (200–210g) of batter into each prepared cake pan and spread evenly. Bake for 11–12 minutes, or until a toothpick inserted in the center comes out clean. The layers are VERY thin, so they shouldn’t need much longer than this. Allow the cakes to cool in the pans for a couple minutes, then carefully invert each onto parchment paper on the counter. Peel off the parchment round from the bottom of the cake; you can reuse it for the next batch or use a new one. Once the pans are cool enough to handle, grease them again, line with parchment rounds, and grease the parchment. Repeat baking the remaining batter until you have baked all 9 layers. Allow all of the cake layers to cool completely, about 1 hour.
Assemble the cake: Carefully place one layer on a serving platter, cake turntable, or cake stand. Spoon and spread 1/4 cup of icing on top, then repeat with the rest of the cake layers and icing. Some icing will spill over the sides and that’s ok. Decorate the top with sprinkles, if desired.
Set the cake aside for at least 1 hour before slicing and serving. This gives the icing time to set and makes the cake easier to slice. You can refrigerate the cake during this time, if desired.
Cover and store leftover cake at room temperature for 1–2 days or in the refrigerator for up to 1 week.
