How to Make It
Prepare the Cake: Preheat oven to 375°F. Whisk together flour, granulated sugar, brown sugar, cocoa, baking soda, and salt in a large bowl. Whisk together butter, water, buttermilk, eggs, and vanilla in a separate bowl. Add butter mixture to flour mixture; stir just until combined. (Some small lumps may remain.) Stir in chocolate chips just until incorporated. Spread batter in a 15- x 10-inch jelly roll pan well coated with baking spray. Bake in preheated oven until a wooden pick inserted in center comes out with moist crumbs, 18 to 20 minutes. Cool completely in pan on wire rack, about 45 minutes.
Prepare the Frosting: Melt butter in a small saucepan over medium-high until butter starts to foam, about 1 minute. Reduce heat to medium, and cook, stirring often, until butter turns a light amber color and starts to smell nutty. Remove from heat, and pour into the bowl of a heavy-duty electric stand mixer. Cool butter to room temperature, about 20 minutes. Add powdered sugar, half-and-half, and bourbon. Beat on high speed, stopping to scrape down sides of bowl as necessary, until fluffy and well blended. Set aside.
Prepare the Candied Walnuts: Line a plate or baking sheet with parchment paper. Heat a medium-size nonstick skillet over medium-high. Add walnuts, sugar, and butter; cook, stirring constantly, until butter melts. Continue to cook, stirring often, until sugar melts and turns amber and walnuts are well coated, 5 to 6 minutes. Working quickly, spread walnut mixture on parchment-lined plate, using a spatula or fork to separate mixture into small pieces before sugar hardens. Let stand until sugar hardens and nuts are cool enough to handle, 5 to 7 minutes.
Assemble the Derby Cake: Spread frosting evenly over the cooled cake, and sprinkle evenly with candied walnuts. Place the chocolate chips in a glass measuring cup, and microwave on HIGH in 15-second intervals until melted and smooth. Let stand until cool but still pourable, about 5 minutes. Transfer melted chocolate to a piping bag, and pipe in a decorative pattern over top of cake.