Prepare the chocolate ganache: In a small saucepan, heat the heavy cream over medium heat until it just begins to simmer. Remove from heat immediately.
Place the finely chopped semisweet chocolate in a heatproof bowl. Pour the hot cream over the chocolate and let it sit for 2 minutes to soften the chocolate.
Add the unsalted butter to the bowl and stir gently until the mixture is smooth and glossy. Set aside to cool to room temperature before using as a topping.
Prepare the whipped chocolate frosting: In a large mixing bowl, beat the softened unsalted butter with an electric mixer on medium speed until creamy, about 2 minutes.
Gradually add the sifted powdered sugar and cocoa powder alternately with the whole milk, beating on low speed after each addition until combined.
Add the vanilla extract and increase the mixer speed to high. Beat for 3 to 5 minutes until the frosting is light, fluffy, and spreadable.
To assemble the toppings, spread the whipped chocolate frosting evenly over the cooled chocolate cake surface.
Pour the cooled chocolate ganache over the frosting, allowing it to drip down the sides for a smooth, shiny finish.
Sprinkle the chocolate sprinkles evenly over the ganache while it is still slightly soft to ensure they stick.
Allow the cake to set at room temperature for 30 minutes before serving to let the toppings firm up.