First, make the cake. Position a rack in the center of the oven and preheat the oven to 350°F. Generously spray three 8-inch cake pans with cooking spray and line the bottom of each with a parchment paper circle. Spray the parchment, too.
Mix the dry ingredients. In a medium bowl, whisk together the flour, baking powder, and salt.
Cream the butter and sugars. In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and sugars. Beat on medium until light, fluffy, and doubled in volume, 3 to 4 minutes, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary. Add the eggs, then the buttermilk and vanilla. Reduce the mixer to low and add the eggs one at a time, adding the next egg only after the previous one has been fully incorporated, scraping down the bottom and sides of the bowl after each addition. With the mixer on low, slowly pour in the oil, followed by the buttermilk and vanilla, and beat until the mixture is smooth, 3 to 4 minutes.
Add the dry ingredients. Gradually add the dry ingredients and beat until just combined. Scrape down the bottom and sides of the bowl once more, and beat on low for an additional 30 seconds.
Assemble the cake layers for baking. Divide the batter evenly between the pans; if using a digital scale to measure out layers, note that this recipe makes around 66.5 ounces (1885 grams) of batter—pour 22.15 ounces (628 grams) of batter into each cake pan. Use an offset spatula to spread the cake batter evenly inside the pans and smooth their tops. Bake and cool the cake layers. Bake for 40 to 45 minutes. When done, the top of the cake should bounce back when gently pressed and a skewer inserted into the center of the cake should come out with a few crumbs attached. Cool completely in the pans on a wire rack before frosting. Prep and melt the chocolate for the frosting. In a food processor, pulse the chocolate for a few seconds at a time until chopped into 1- to 2-inch pieces. Transfer the chocolate to the top of a double boiler or to a heatproof bowl set over a medium, heavy-bottomed saucepan filled with a few inches of simmering water (be sure the bottom of the bowl does not touch the water). Cook over medium heat, using a heatproof rubber spatula to stir the mixture and scrape the sides of the bowl occasionally, until the chocolate has melted, about 10 minutes. Set the top of the double boiler or the bowl on a wire rack and let the chocolate cool while you prep the other ingredients. Make the chocolate frosting. In the food processor, combine the confectioners’ sugar, butter, milk, vanilla, and salt. Pour in the melted chocolate and pulse briefly to combine, then process until the frosting is creamy, smooth, and light brown in color, about 5 minutes. Scrape down the bottom and sides of the bowl with a rubber spatula, then process for an additional 30 seconds. Assemble the cake. If necessary, level the top of the cakes. Place one of the cake layers on a cake board or serving platter in the center of a rotating cake stand. Use a rubber spatula or cookie dough scoop to drop ½ cup of frosting in the middle of this cake layer. Use an offset spatula to spread it evenly all over the top, just like you would spread butter on toast. Place the second cake on top of this frosting, stacking it evenly on top of the first cake. Use the rubber spatula or cookie dough scoop to drop another ½ cup of frosting in the middle of this cake layer. Spread it evenly all over the top. Finally, place the third cake on top of this frosting, stacking it evenly on top of the first two cakes. Next, crumb coat the cake. Use the offset spatula to cover the surface of the entire layer cake with a thin layer of frosting. Use just enough frosting to cover the entire cake completely. Refrigerate, uncovered, for 10 to 15 minutes to stiffen and "set" the frosting.
After the crumb coat sets, finish frosting the cake. Use the offset spatula to cover the cake with the remaining frosting. Then, use the spatula to make large, random sweeping motions across the frosting on the top and sides of the cake. The sweeping motions will create swirls.
Serve and store. Serve immediately. The assembled yellow cake with chocolate frosting can be stored at room temperature, under a cake dome or a large bowl turned upside down, for up to 1 day. Press a sheet of plastic wrap against any cut surfaces to prevent the cake from drying out. After that, cover the entire cake loosely with plastic wrap and refrigerate for up to 2 days.