Making the Cake:
Preparation:
Preheat your oven to 350°F (175°C) and position the oven rack in the middle. Lightly grease an 18- by 13-inch rimmed baking sheet to ensure the cake doesn’t stick.
Dry Ingredients:
In a large mixing bowl, combine the flour, sugar, baking soda, and salt. Mix well to ensure even distribution of the baking soda and salt.
Wet Ingredients:
In another bowl, whisk together the eggs, egg yolks, vanilla extract, and sour cream until you have a smooth mixture. This will help in achieving a uniform batter later.
Chocolate Mixture:
In a large saucepan, combine the chopped semisweet chocolate, unsalted butter, vegetable oil, water, and cocoa powder. Heat over medium heat, stirring occasionally, until the mixture is completely smooth and glossy. This should take about 3 to 5 minutes.
Combine Mixtures:
Gradually whisk the chocolate mixture into the flour mixture until well combined. Then, slowly whisk in the egg mixture until you have a smooth, lump-free batter.
Bake:
Pour the batter into the prepared baking sheet, spreading it out evenly. Bake for 18 to 20 minutes, or until a toothpick inserted into the center comes out clean. Transfer the cake to a wire rack to cool slightly.
Making the Icing:
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