Brooklyn Blackout Cake

Ingredients

• 1-3/4 cups water plus 1/4 cup water, separated
• 1-3/4 cups granulated sugar
• 1/2 Tbsp light corn syrup
• 1/2 cup unsweetened cocoa powder
• scant 1/3 cup cornstarch
• 3 Tbsp unsalted butter, cold and cut into 1-inch cubes
• 1/4 tsp pure vanilla extract
• 3-1/2 Tbsp unsalted butter, at room temperature
• 10 Tbsp granulated sugar
• 1 egg, room temperature
• 1/4 tsp vanilla extract
• 1/6 cup unsweetened cocoa powder
• scant 1/2 tsp baking powder
• scant 1/2 tsp baking soda
• a pinch of salt
• 1 1/3 cups all-purpose flour
• 2/3 cup whole milk