First, assemble the cake. If necessary, level the top of both cakes. Place one of the cake layers on a cake board or serving platter in the center of a rotating cake stand. Use a rubber spatula or cookie dough scoop to drop ½ cup of frosting in the middle of this cake layer. Spread it evenly all over the top, just like you would spread butter on toast. Place the second cake on top of this frosting, stacking it evenly on top of the first cake.
Next, crumb coat the cake. Cover the surface of the entire layer cake with a thin layer of frosting. Use just enough frosting to cover the entire cake completely. Refrigerate, uncovered, for 30 minutes to stiffen and "set" the frosting.
After the crumb coat sets, finish frosting the cake. Scoop out ⅓ cup of the sweetened condensed milk frosting and place it in a separate bowl; reserve this for the chocolate fudge swirls. Place the cake back in the center of the rotating cake stand. Cover the cake completely with the remaining frosting, using an offset spatula to spread the frosting all over the top and sides of the cake evenly. Once the cake is completely covered, hold the length of the offset spatula's blade against the frosting as you rotate the cake stand to smoothen the frosting. Once the frosting is perfectly smooth, refrigerate the cake while you prepare the chocolate fudge swirls. Make the chocolate fudge swirls. In a small bowl, whisk together the chocolate sauce and coffee until combined. Divide the reserved sweetened condensed milk frosting and between two small bowls. In one bowl, use a small rubber spatula to mix in 1 to 2 teaspoons of the chocolate coffee sauce until pale brown and creamy. In the second bowl, use the rubber spatula to mix in 1 to 2 Tablespoons of chocolate coffee sauce until dark brown and creamy.
Decorate the cake. Remove the cake from the refrigerator and place it back in the center of the rotating cake stand. Use the offset spatula to dab about 1 teaspoon of frosting at the top edge of the cake, rotating from each different bowl of frosting so that you have different colored dollops of frosting next to each other. Continue dabbing until you have a border of these dollops around the top of the cake.
After you've bordered the cake, use the offset spatula to carefully swipe each of the dollops down the cake in a diagonal motion, rotating the cake stand slowly to help. Repeat until all the dollops are even, but try not to overwork it or you might lose some of the "barely stirred" pattern you're going for. Smoothen any leftover mocha dollops at the top of the cake, rotating the cake stand in a circle to create a spiral motion at the top of the cake. Use the remaining chocolate sauce and chocolate fudge frostings to cover the top of the cake completely.
Serve immediately. The assembled Vietnamese iced coffee cake can be stored at room temperature, under a cake dome or a large bowl turned upside down, for up to 1 day. Press a sheet of plastic wrap against any cut surfaces to prevent the cake from drying out. After that, cover the entire cake loosely with plastic wrap and refrigerate for up to 2 days.