1/2cup (4-ounces) unsalted butter, at room temperature
1cup (7 1/2-ounces) firmly packed light brown sugar
3/4cup (5 1/4-ounces) granulated sugar
1/2cup canola oil
3-- egg yolks, at room temperature
3-- eggs, at room temperature
-- Raspberry Buttercream
Center an oven rack and preheat the oven to 350F. Grease 3 (8 by 2-inch) round cake pans and line bottom with parchment paper circles. Grease parchment paper.
Put the unsweetened chocolate and the cocoa into a small bowl. Pour the boiling water over the chocolate and allow it to steep for 1 minute. Whisk the mixture together. Whisk in the sour cream and vanilla. Set aside.
Sift together the flour, baking soda, and salt in a bowl, then whisk the mixture by hand to ensure that the ingredients are well mixed.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and both sugars together on medium-high speed until light, about 3 minutes. As you make the batter, stop the mixer frequently and scrape the paddle and the sides of the bowl with a rubber spatula. On low speed, drizzle the oil into the mixture until blended. Turn the mixer up to medium-high speed and beat until the batter is fluffy, about 3 more minutes. Blend in the eggs and egg yolks one at a time, adding the next one as soon as the previous one has disappeared into the batter. With the mixer on low speed, add the flour mixture in three parts, alternating with the chocolate mixture in two parts, beginning and ending with the flour. After each addition, mix until just barely blended and stop and scrape the bowl. Stop the mixer before the last of the flour has been incorporated and complete the blending by hand with a rubber spatula to ensure you do not overbeat the batter.
Divide the thick batter equally among the prepared pans (there will be approximately 1 pound 2 ounces per pan). Smooth the tops and tap the pans on the counter to settle the batter and eliminate any large air bubbles. Bake in the middle of the oven until the centers spring back when lightly touched, 22 to 25 minutes. Cool the cakes in their pans on a wire rack for 30 minutes. Flip the cakes out of the pans, leaving on the parchment paper until you assemble the cake. Let them continue to cool on the rack, top sides up, until they reach room temperature.
To assemble the cake, lay one of the cakes top side up on a cake plate. Using a metal spatula, frost the top with 3/4 cup of Raspberry Buttercream (see recipe for Basic Buttercream), spreading it out to the edge of the cake (the filling will be about 1/4 inch thick). Stack the second cake top side up on top of the frosted cake and spread another 3/4 cup of buttercream on top of it. Stack the last layer of cake top side up on top. Look for any frosting that may have oozed out beween the layers and spread it along the sides of the cake. Apply a thin layer of frosting all over the cake to create a “crumb coat.” Place the cake in the refrigerator until the frosting is firm, about 10 minutes. Take it out and frost the cake with the remaining buttercream, using your spatula to make decorative swirls (for additional guidance on how to frost a cake, see page 10).
Store the cake in an airtight container at room temperature for up to 3 days.