Prepare the oven: Preheat oven to 350°F (175°C). Grease and flour a 10x15-inch jelly roll pan.
Make the chocolate base: In a medium saucepan, combine butter, water, and cocoa powder. Bring just to a boil, stirring until smooth. Remove from heat and set aside.
Mix dry ingredients: In a large bowl, whisk together flour, granulated sugar, brown sugar, baking soda, salt, and instant coffee (if using).
Add wet ingredients: Stir in sour cream, eggs, and vanilla until smooth. Slowly pour in the warm chocolate mixture, whisking until fully combined.
Bake the cake: Pour batter into the prepared pan and bake for 22–25 minutes, or until a toothpick inserted in the center comes out clean.
Prepare the frosting: While the cake bakes, heat milk, butter, and cocoa in a saucepan until the butter melts. Remove from heat, whisk in powdered sugar and vanilla until smooth.
Frost the cake: Spread frosting over the warm cake. Sprinkle toasted pecans on top if desired.
Serve: Allow frosting to set for 10–15 minutes before slicing into squares.