Preheat the oven to 350 degrees °F. Grease and flour the baking pan.
Beat cake mix, water, eggs, oil, cooled instant coffee, and cocoa powder in a large bowl with an electric mixer on low speed until moistened. Beat on high speed for 2 minutes. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center of cake comes out clean, for about 40.
Meanwhile, combine sweetened condensed milk, butter, and egg yolk in a medium saucepan over medium heat; cook and stir until thickened, about 6 minutes.
Allow frosting to cool slightly.
Spread frosting over warm cake and sprinkle the top of the cake with roasted hazelnuts.