Adjust your oven rack to the middle position and preheat to 350°F. Grease a heavy 18×13-inch rimmed half-sheet baking pan.

In a large bowl, thoroughly whisk together the all-purpose flour, granulated sugar, baking soda, and salt. Set aside. In a separate medium bowl, whisk the whole eggs, extra yolks, 2 teaspoons of vanilla extract, and full-fat sour cream together until completely smooth and unified.

Combine the chopped semisweet chocolate, 4 tablespoons of butter, vegetable oil, water, and ½ cup of Dutch-processed cocoa powder in a large saucepan over medium heat. Pro Tip: Bringing these ingredients to a simmer does more than melt the solid chocolate—the hot oil and boiling water actively "bloom" the cocoa powder. This intense thermal contact dissolves the starch hulls around the cocoa cells, releasing deeply trapped, complex chocolate volatile aromas that dry mixing cannot achieve.

Remove the chocolate mixture from the heat once completely smooth (about 3 to 5 minutes). Immediately pour the hot liquid chocolate straight into the dry flour bowl, whisking continuously until just combined.

Whisk the prepared egg and sour cream mixture directly into the warm chocolate batter. Crucial: Ensure your sour cream and eggs are at room temperature so they integrate seamlessly without shocking and curdling the hot chocolate base. Pour the glossy, runny batter onto the prepared sheet pan.

Bake for 18 to 20 minutes until the top springs back lightly when pressed or a toothpick inserted in the center emerges clean. Transfer the pan to a wire rack.

The Molten Capillary Integration: While the cake has exactly 5 minutes left in the oven, prepare the frosting. Melt 1 stick of butter with the heavy cream, ½ cup of cocoa powder, and light corn syrup in a saucepan over medium heat, whisking until smooth. Remove from the heat and vigorously beat in the confectioners' sugar and 1 tablespoon of vanilla. The absolute second the cake comes out of the oven, dump the hot, liquid icing over the surface and smooth it to the edges with an offset spatula. The heat expands the cake's surface pores, allowing the hot icing to fuse straight down into the upper crumb.

Shower the molten icing immediately with the toasted, chopped pecans so they lock into the setting glaze layer. Let the cake cool completely to room temperature before slicing into dense, fudgy squares.