Preheat oven to 350°F (175°C) and generously grease and flour a 10x15 jelly roll pan or coat with baking spray. In a medium saucepan over low heat, combine butter, water, and cocoa powder, stirring occasionally until the butter is completely melted. Increase heat to medium and bring the mixture to a gentle boil, then remove from heat and let cool for 15–20 minutes. While the chocolate mixture cools, whisk together flour, granulated sugar, light brown sugar, baking soda, salt, and instant coffee in a large bowl. In a separate bowl, whisk together sour cream, eggs, and vanilla extract, then incorporate this into the dry ingredients until just blended. Stir the cooled chocolate mixture into the batter and mix until smooth and cohesive. Spread the batter evenly in the prepared pan and bake for 18–22 minutes or until a toothpick inserted in the center emerges clean or with a few moist crumbs. As the cake bakes, prepare the frosting by warming milk and butter in a medium saucepan over medium-low heat until the butter melts. Remove from heat, whisk in cocoa powder until fully incorporated, then add powdered sugar and vanilla, whisking until smooth and pourable. Immediately pour the warm frosting over the hot cake, then sprinkle with toasted pecans if desired. Allow the frosting to set for about an hour before slicing and serving.