Preheat the oven to 350 degrees F / 175 degrees C. Generously grease the three 8-inch / 20cm cake pans, then line them with greased parchment paper.
In a stand mixer fitted with the paddle attachment, cream the butter on medium-high speed until creamy and smooth, about 1 minute.
Turn the mixer speed to medium, add the oil and sugar to the butter, and beat for about 5 minutes, until the mixture is light in color and about double in volume.
Turn the speed to medium-low and add the eggs and egg yolks, one at a time, mixing each until incorporated before adding the next. Scrape the bowl after each addition.
In a medium bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and salt until well combined.
In a liquid measuring cup, whisk together the milk and sour cream.
Add one-third of the flour mixture to the butter mixture and mix until combined. Scrape the bowl and add half of the milk mixture, mixing until combined. Repeat with another one-third flour, the remaining milk mixture, and then finish with the final one-third flour. Scrape the bowl after each addition.
Divide the batter into the prepared pans and spread evenly using an offset spatula. Gently tap the pans on the counter several times to release excess air bubbles.
Bake until a tester comes out clean, about 30 minutes. Allow the cakes to cool in the pans for 15 minutes, then transfer to a wire rack to cool completely.
Remove the parchment paper and place one cake layer on a serving plate.
Make the frosting: In a medium saucepan over low heat, combine the cream, butter, espresso powder, and salt and bring to a gentle simmer, stirring often until the butter is melted. Add the chocolate and swirl the pan until the chocolate is submerged in the hot cream. Let the mixture sit for about 3 minutes, then whisk until smooth.
Pour the mixture into the bowl of a stand mixer fitted with the paddle attachment. Let the mixture cool to room temperature; it will become quite thick as the butter and chocolate set.
Turn the mixer speed to low, add the confectioners' sugar, a little at a time, and beat until smooth and spreadable. If the frosting is at all grainy, add additional cream, 1 tablespoon at a time, until it's smooth. The frosting will be quite soft but firm enough to cling to the cake and spread evenly. Use immediately.
Using a metal decorating spatula, spread 1/4-inch / 6mm-thick layer of the frosting over the cake, making sure it goes all the way to the edge. Place the next cake over the frosting and top with another layer of frosting. Repeat with the last cake. If desired, at this point, you could crumb-coat the cake.
Decorate the cake with a smooth layer of the remaining frosting. Top with marshmallows.
Serve the cake immediately or store at room temperature, covered, for up to 48 hours.