Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 10x15 inch pan. Alternatively, line a 10x15 pan with parchment paper.
Melt the 1 cup unsalted butter on low in a saucepan, add the 1 cup water and 5 tablespoons unsweetened cocoa powder. Bring mixture to a boil then remove from heat. Set aside.
In a small bowl, whisk together 1/2 cup sour cream and 2 large eggs.
Combine the 2 cups all purpose flour, 2 cups granulated sugar, 1 teaspoon baking soda and 1/2 teaspoon salt in the bowl of a stand mixer. Beat in the sour cream and egg mixture. Once the cocoa powder mixture is cool enough to touch, beat it into the four mixture on low speed. Scrape sides and beat just until fully mixed.
Pour batter into prepared pan. Bake in the preheated oven for 22-25 minutes, or until a toothpick inserted into the center comes out clean.
About half way through the cooking process, make the frosting.
To make the frosting, combine 6 tablespoons whole milk, additional 5 tablespoons unsweetened cocoa powder, and additional 1/2 cup unsalted butter. Bring to a boil, then remove from heat. Stir in the 4 cups confectioners sugar and 1 teaspoon pure vanilla extract, then fold in the 1 cup pecans, mixing until blended. Spread frosting over warm cake.