For the Cake: Adjust oven rack to middle position and heat oven to 350°F Grease 18 x 13 inch rimmed baking sheet. Combine flour, sugar, baking soda, and salt in large bowl. Whisk eggs and yolks, vanilla, and sour cream in another bowl until smooth.
Heat chocolate, butter, oil, water, and cocoa in large saucepan over medium heat, stirring occasionally, until smooth, 3-5 minutes. Whisk chocolate mixture into flour mixture until incorporated. Whisk egg mixture into batter, then pour into prepared baking pan. Bake until toothpick inserted into center comes out clean, 18-20 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. Off heat, whisk in confectioners'sugar and vanilla. Spread warm icing evenly over hot cake and sprinkle with pecans. Let cake cool to room temperature on wire rack, about 1 hour, then refrigerate until icing is set, about 1 hour longer. (Cake can be wrapped in plastic and refrigerated for up to 2 days. Bring to room temperature before serving). Cut into 3-inch squares.