For the cake: Adjust oven rack to middle position and heat oven to 350 degrees. Grease an 18- by 13-inch rimmed baking sheet. In a large bowl combine flour, sugar, baking soda, and salt;set aside. In a another bowl whisk eggs and yolks, vanilla, and sour cream until smooth.
Heat chocolate, butter, oil, water, and cocoa in a large saucepan over medium heat, stirring occasionally, until smooth, 3 to 5 minutes. Whisk chocolate mixture into flour mixture until combined. Whisk egg mixture into batter, then pour into prepared baking pan. Bake until toothpick inserted into center comes out clean, 18 to 20 minutes. Transfer to wire rack.
For the icing: About 5 minutes before cake is done, heat butter, cream, cocoa, and corn syrup in large saucepan over medium heat, stirring occasionally, until smooth. Turn off heat and whisk in confectioners’ sugar and vanilla. Spread warm icing evenly over hot cake with an offset spatula and sprinkle with toasted pecans. Let cake cool to room temperature on wire rack, about 1 hour, then refrigerate until icing is set. (Cake can be wrapped in plastic and refrigerated for up to 2 days. Bring to room temperature before serving.) Cut into 3-inch squares. Serve.